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Question 1Nature and Scope of Logic; Logic and Language
Which of the following best states the traditional definition of logic as a branch of philosophy?
- The science of the necessary laws of thought and the study of valid inference Correct answer.
- The art of persuading an audience by appealing to emotion
- The empirical study of how people actually form beliefs
- The grammar of a particular natural language
Explanation
Logic is traditionally defined as the science of the laws of thought insofar as those laws govern valid inference, so its central concern is the relation of premises to conclusion. Persuasion, empirical belief formation and grammar belong to rhetoric, psychology and linguistics respectively.
Question 2Nature and Scope of Logic; Logic and Language
A student says that logic is a normative rather than a descriptive science. What does this claim mean?
- Logic describes the customs of a society and has no standards
- Logic describes the physical causes of thinking in the brain
- Logic prescribes only the grammar of a language
- Logic prescribes how reasoning ought to proceed, not merely how people do reason Correct answer.
Explanation
A normative discipline sets standards or norms for correct performance, so logic is normative because it specifies when an inference is valid, independent of whether people actually reason that way. Descriptive sciences report facts about actual behaviour.
Question 3Nature and Scope of Logic; Logic and Language
Which pair correctly distinguishes the two main divisions of logic traditionally recognised in the higher secondary syllabus?
- Formal logic, which studies the form of arguments, and material logic, which studies their content and truth Correct answer.
- Inductive logic, which studies deduction, and deductive logic, which studies induction
- Symbolic logic, which studies language, and rhetorical logic, which studies style
- Ancient logic, which studies validity, and modern logic, which studies persuasion
Explanation
Formal logic abstracts from content and examines the structure that makes an argument valid, while material logic is concerned with the actual subject matter and truth of the premises. The two are complementary rather than opposed.
Question 4Nature and Scope of Logic; Logic and Language
An argument is said to be valid when which condition holds?
- Its premises make the conclusion probable to a high degree
- It is impossible for all the premises to be true and the conclusion false Correct answer.
- Its premises are in fact true in the actual world
- Its conclusion is accepted by most competent speakers
Explanation
Validity is a matter of the necessary connection between premises and conclusion: if the premises were true, the conclusion could not be false. Truth of premises is a separate question, and probability belongs to inductive strength.
Question 5Nature and Scope of Logic; Logic and Language
Consider the argument: 'All poets are dreamers; some dreamers are careless; therefore some poets are careless.' How should this argument be assessed?
- Valid, because both premises are particular
- Invalid, because the middle term is not distributed in either premise Correct answer.
- Invalid, because the conclusion is negative while the premises are affirmative
- Sound, because the conclusion follows from the premises
Explanation
In this syllogism the middle term 'dreamers' occurs as the predicate of two affirmative premises, so it is undistributed twice and cannot link the extremes. The careless dreamers may lie entirely outside the class of poets.
Question 6Nature and Scope of Logic; Logic and Language
Which statement correctly expresses the relation between truth and validity?
- Every argument with true premises and a true conclusion is valid
- Validity requires that the conclusion be true independently of the premises
- Every valid argument has true premises and a true conclusion
- An argument may be valid with false premises, but a sound argument must have true premises and a valid form Correct answer.
Explanation
Validity concerns only the form, so premises may be false while the inference remains valid. Soundness adds the further requirement that the premises actually be true, which guarantees a true conclusion.
Question 7Nature and Scope of Logic; Logic and Language
Which of the following is the best example of an argument in the logical sense rather than a mere collection of statements?
- Copper is a metal; copper is reddish; copper conducts electricity
- Since every metal expands when heated, and copper is a metal, copper expands when heated Correct answer.
- Please weigh the copper sample carefully before the demonstration
- Copper expands when heated, which is interesting and useful
Explanation
An argument requires premises offered as support for a conclusion, signalled here by 'since' and 'therefore' in effect. A list of facts, a command and a remark lack that inferential claim.
Question 8Nature and Scope of Logic; Logic and Language
In the sentence 'The word "logic" derives from the Greek logos', the word 'logic' occurs in which use?
- Neither use nor mention, since it is a quotation
- Both use and mention at once
- Use, because it names the subject being discussed
- Mention, because it is referred to rather than used to speak about reasoning Correct answer.
Explanation
A term is used when it refers to what it normally denotes and mentioned when it is itself the object of discussion, conventionally marked by quotation marks. Here the quoted word is the subject of the sentence, so it is mentioned.
Question 9Nature and Scope of Logic; Logic and Language
Which pair correctly matches a sentence with its function in logic?
- 'Shut the door' is exclamatory; 'Is the door shut?' is imperative; 'The door is shut' is declarative
- 'Shut the door' is interrogative; 'Is the door shut?' is declarative; 'The door is shut' is imperative
- 'Shut the door' is declarative; 'Is the door shut?' is imperative; 'The door is shut' is interrogative
- 'Shut the door' is imperative; 'Is the door shut?' is interrogative; 'The door is shut' is declarative Correct answer.
Explanation
Logic deals primarily with declarative sentences, since only they can be true or false and thus serve as premises or conclusions. Imperatives issue commands and interrogatives ask questions, so neither asserts a proposition.
Question 10Nature and Scope of Logic; Logic and Language
A proposition is best characterised in logic as which of the following?
- The physical marks or sounds that make up a sentence
- The emotional tone a speaker conveys
- The grammatical subject of a sentence
- The meaning or truth-bearing content expressed by a declarative sentence Correct answer.
Explanation
A proposition is what a declarative sentence says, and it is this content that is true or false. Different sentences in different languages can express one and the same proposition.
Question 11Nature and Scope of Logic; Logic and Language
Which of the following best illustrates the distinction between a sentence and a proposition?
- 'It is raining' and 'It is raining' are two different propositions
- Every sentence expresses exactly one proposition and no sentence expresses more
- 'It is raining' and 'Barsha ho rahi hai' express the same proposition in two languages Correct answer.
- A proposition is always longer than the sentence that expresses it
Explanation
The sentence is a linguistic item belonging to a particular language, while the proposition is the meaning it carries. Translation preserves the proposition while changing the sentence.
Question 12Nature and Scope of Logic; Logic and Language
The word 'bank' in 'He sat on the bank of the river' and in 'She deposited money in the bank' illustrates which feature of language relevant to logic?
- Ambiguity, because one word form carries two distinct meanings Correct answer.
- Synonymy, because the two occurrences mean the same thing
- Emotive meaning, because the word expresses feeling
- Vagueness, because the word has no precise boundary in either case
Explanation
Ambiguity occurs when a single expression has more than one distinct meaning, as with 'bank' meaning river edge and financial institution. Logic must disambiguate such terms before assessing an argument, since the two meanings support different inferences.
Question 13Nature and Scope of Logic; Logic and Language
Which statement correctly distinguishes vagueness from ambiguity?
- A vague term has one meaning with unclear boundaries, while an ambiguous term has two or more distinct meanings Correct answer.
- A vague term has several unrelated meanings, while an ambiguous term has no meaning at all
- Vagueness and ambiguity are the same defect under different names
- Vagueness applies only to sentences and ambiguity only to single words
Explanation
Vagueness arises where a single sense admits borderline cases, as with 'bald' or 'heap'. Ambiguity arises where one expression has more than one sense, as with 'light' meaning not heavy or not dark.
Question 14Nature and Scope of Logic; Logic and Language
In logic, the 'informal fallacies' are so called because they
- occur only in informal conversation and never in written work
- cannot be explained or classified at all
- are errors of grammar rather than of reasoning
- depend on the content and context of the reasoning rather than on its bare form alone Correct answer.
Explanation
Informal fallacies such as appeal to authority or begging the question are detected by attending to meaning, context and the substance of the argument, not merely to its schema. Formal fallacies, by contrast, are identifiable from the logical form alone.
Question 15Nature and Scope of Logic; Logic and Language
A speaker argues: 'You cannot trust his view on the tax bill, because he has never held public office.' Which fallacy is committed?
- Hasty generalisation, since a general rule is drawn from one case
- Begging the question, since the conclusion is assumed in the premise
- False dilemma, since only two options are presented
- Ad hominem, since the argument attacks the person rather than the merits of the view Correct answer.
Explanation
Ad hominem reasoning rejects a claim by citing a feature of the person advancing it rather than by addressing the evidence for the claim. The speaker's lack of office is irrelevant to whether the tax analysis is correct.
Question 16Nature and Scope of Logic; Logic and Language
Which argument commits the fallacy of begging the question?
- Free trade is beneficial because several economists endorse it
- Free trade is beneficial because unrestricted commerce brings advantages Correct answer.
- Free trade is beneficial because tariffs have historically reduced trade volumes
- Free trade is beneficial because it lowers prices for consumers
Explanation
Begging the question occurs when the premise merely restates the conclusion in different words, giving no independent support. 'Unrestricted commerce brings advantages' says no more than that free trade is beneficial.
Question 17Nature and Scope of Logic; Logic and Language
The distinction between the 'extension' and the 'intension' of a general term is best captured by which pair?
- Extension: the attributes of a thing; intension: the number of letters in the term
- Extension: the truth value of the sentence; intension: its length
- Extension: the class of objects the term applies to; intension: the set of attributes that determines membership in that class Correct answer.
- Extension: the emotional force of the term; intension: its grammatical gender
Explanation
The extension of 'mammal', for instance, is the class of all mammals, while its intension is the defining property of being a warm-blooded animal that suckles its young. Intension determines extension.
Question 18Nature and Scope of Logic; Logic and Language
Which of the following terms is used distributively rather than collectively in the statement given?
- 'Committee' in 'The committee reached a single decision'
- 'Team' in 'The team won the match together'
- 'Crowd' in 'The crowd broke through the barrier'
- 'Student' in 'Every student in the class passed the test' Correct answer.
Explanation
A term is distributive when what is predicated of it applies to each member individually, as with each student passing. Collective terms predicate something of the group as a whole, which need not hold of any member.
Question 19Nature and Scope of Logic; Logic and Language
The definition 'A triangle is a plane figure bounded by three straight lines' is best classified as which kind of definition?
- Ostensive definition, pointing to an example
- Essential or real definition, stating the nature of the thing defined Correct answer.
- Nominal definition, merely stipulating the meaning of a word
- Persuasive definition, smuggling in an evaluative attitude
Explanation
An essential definition states the genus and the differentia that constitute what the thing is, here plane figure with three straight sides. A nominal definition would only fix how a word is to be used.
Question 20Nature and Scope of Logic; Logic and Language
Which rule of definition is violated by 'A dog is an animal that is not a cat'?
- A definition should not be too broad
- A definition should not be circular
- A definition should not be negative where the term defined is positive Correct answer.
- A definition should not be expressed obscurely
Explanation
Definitions should state what a thing is rather than what it is not, since a negative formula excludes without explaining. Saying a dog is not a cat fails to state the nature of a dog at all.
Question 21Nature and Scope of Logic; Logic and Language
In the statement 'All that glitters is not gold', the ambiguity most relevant to logical analysis lies in
- the meaning of the word 'glitters', which is vague
- the scope of the negation, which may range over the whole sentence or only over the predicate Correct answer.
- the use of the copula 'is', which is always ambiguous
- the reference to gold, which is a collective term
Explanation
The sentence can be read as 'Not everything that glitters is gold' or, less naturally, as 'Nothing that glitters is gold'. The difference turns on whether the negation governs the whole proposition or only the predicate, a classic case of scope ambiguity.
Question 22Nature and Scope of Logic; Logic and Language
Which of the following best explains why logic is said to be concerned with the form rather than the matter of arguments?
- Because validity depends on the arrangement of terms and connectives, which can be exhibited by replacing content words with symbols Correct answer.
- Because logic requires that all premises be true before an argument can be examined
- Because logic studies only arguments written in symbolic notation
- Because logic ignores meaning entirely and studies only printed shapes
Explanation
By substituting letters for content words, logic isolates the pattern that guarantees the conclusion, such as 'All M are P; all S are M; therefore all S are P'. Any argument of that pattern is valid whatever the actual subject matter.
Question 23Nature and Scope of Logic; Logic and Language
The sentence 'The present King of France is bald' raises a problem for logic mainly because
- the word 'bald' is too vague to be analysed
- a declarative sentence may presuppose the existence of something that does not exist, complicating its truth value Correct answer.
- the sentence is imperative in form and so has no truth value
- the sentence contains a grammatical error that prevents formalisation
Explanation
Standard subject-predicate analysis suggests that the sentence is about something, yet there is no present King of France. Logic must decide whether the sentence is false or fails to express a proposition, which is why presupposition and existence claims matter in the analysis of language.
Question 24Nature and Scope of Logic; Logic and Language
A term is said to be 'categorical' in a proposition when the proposition
- asserts or denies a predicate of a subject without condition Correct answer.
- asks a question about the subject
- expresses a condition under which something would be true
- expresses a command about the subject
Explanation
Categorical propositions such as 'All metals are conductors' assert a predicate of a subject unconditionally, and they form the basis of the traditional square of opposition. Conditional propositions, by contrast, assert that one thing holds if another does.
Question 25Terms, Propositions and Classification of Propositions
In logic, what does the term 'proposition' refer to?
- An exclamation that expresses sudden emotion
- A word used to name a person, place, or thing
- A command that directs someone to perform an action
- A sentence that expresses a complete thought and can be judged true or false Correct answer.
Explanation
A proposition is the meaning-content of a declarative sentence, and it is the kind of thing that is either true or false. Commands, questions, and exclamations lack truth value, so they are not propositions.
Question 26Terms, Propositions and Classification of Propositions
Which of the following is a proposition in the strict logical sense?
- Please close the door.
- How beautiful the sunrise is!
- Guwahati is the capital of Assam. Correct answer.
- Is the library open today?
Explanation
Only a declarative sentence asserts something that can be true or false, and the sentence about Guwahati does exactly that. Requests, questions, and exclamations are not truth-bearers and so fall outside the class of propositions.
Question 27Terms, Propositions and Classification of Propositions
What is a term in logic?
- A connective that joins two propositions together
- A complete assertion that can be judged true or false
- A conclusion drawn from two premises
- A word or group of words that can serve as the subject or predicate of a proposition Correct answer.
Explanation
Terms are the building blocks of propositions: they name or denote something and can occupy the subject or predicate position. A proposition is built from terms, while a connective links propositions and a conclusion is argued to.
Question 28Terms, Propositions and Classification of Propositions
Which classification of propositions is based on quantity alone?
- Necessary and contingent
- Affirmative and negative
- Universal, particular, and singular Correct answer.
- Categorical and hypothetical
Explanation
Quantity concerns how much of the subject class the predicate is said of, giving universal, particular, and singular propositions. Affirmative/negative is quality, while the other pairs are different divisions altogether.
Question 29Terms, Propositions and Classification of Propositions
The proposition 'No reptiles are warm-blooded animals' is classified by quality as which of the following?
- Negative Correct answer.
- Affirmative
- Hypothetical
- Particular
Explanation
Quality depends on whether the predicate is affirmed or denied of the subject, and 'No...are' explicitly denies the predicate. Quantity and form are separate questions, so the answer rests only on the denial.
Question 30Terms, Propositions and Classification of Propositions
How many terms does a standard categorical proposition contain?
- Three
- Two Correct answer.
- Four
- One
Explanation
A standard categorical proposition relates exactly two terms, a subject term and a predicate term. Three terms appear only in a categorical syllogism, where a middle term is added.
Question 31Terms, Propositions and Classification of Propositions
Which word is the copula in the proposition 'All metals are conductors'?
- Metals
- Conductors
- Are Correct answer.
- All
Explanation
The copula is the linking word that affirms or denies the predicate of the subject; here 'are' performs that role. 'All' is a quantifier, 'metals' the subject term, and 'conductors' the predicate term.
Question 32Terms, Propositions and Classification of Propositions
What distinguishes a singular proposition from a universal proposition?
- A singular proposition has no predicate term
- A singular proposition always lacks a copula
- A singular proposition has a proper name or definite description as subject and refers to one individual Correct answer.
- A singular proposition is always negative in quality
Explanation
A singular proposition picks out exactly one individual in its subject, as with a proper name, whereas a universal proposition speaks of a whole class. Logically the singular proposition is often treated like a universal, but its subject still denotes one thing.
Question 33Terms, Propositions and Classification of Propositions
In traditional logic, a singular proposition such as 'Socrates is mortal' is usually treated as equivalent to which type?
- A particular proposition
- A disjunctive proposition
- A universal proposition Correct answer.
- A hypothetical proposition
Explanation
Because the subject picks out the whole of its (single-membered) class, the singular proposition is conventionally assimilated to the universal form. This lets it enter syllogistic reasoning under the rules for universal propositions.
Question 34Terms, Propositions and Classification of Propositions
What is the logical form of an A proposition?
- All S is P Correct answer.
- No S is P
- Some S is not P
- Some S is P
Explanation
In the traditional square of opposition, A is the universal affirmative, expressed as 'All S is P'. The other forms are E (universal negative), I (particular affirmative), and O (particular negative).
Question 35Terms, Propositions and Classification of Propositions
Which proposition is an O proposition?
- All students are diligent.
- Some students are not diligent. Correct answer.
- Some students are diligent.
- No students are diligent.
Explanation
The O proposition is the particular negative, denying the predicate of part of the subject class, as in 'Some students are not diligent'. Its quantity is particular and its quality negative.
Question 36Terms, Propositions and Classification of Propositions
The proposition 'Some politicians are honest' has which combination of quantity and quality?
- Universal affirmative
- Particular affirmative Correct answer.
- Particular negative
- Universal negative
Explanation
The word 'some' marks particular quantity because it speaks of an indefinite part of the class. The copula 'are' affirms the predicate, giving affirmative quality, so the proposition is an I proposition.
Question 37Terms, Propositions and Classification of Propositions
What does 'distribution of a term' mean in categorical logic?
- A term is distributed when it is replaced by a pronoun
- A term is distributed when it is the predicate of an affirmative proposition
- A term is distributed when it refers to all the members of the class it denotes Correct answer.
- A term is distributed when it appears in both premises of an argument
Explanation
Distribution concerns reference: a term is distributed if the proposition says something about every member of the class the term denotes. This property is fixed by the form of the proposition and is central to testing syllogisms.
Question 38Terms, Propositions and Classification of Propositions
In the proposition 'All birds are creatures that lay eggs', which terms are distributed?
- Both subject and predicate terms
- Only the subject term Correct answer.
- Neither term
- Only the predicate term
Explanation
In a universal affirmative (A) proposition, the subject term is distributed because the predicate is affirmed of every bird, but the predicate is undistributed because the class of egg-laying creatures is not exhausted by birds.
Question 39Terms, Propositions and Classification of Propositions
Which proposition distributes both its subject term and its predicate term?
- No poets are dreamers. Correct answer.
- Some poets are dreamers.
- All poets are dreamers.
- Some poets are not dreamers.
Explanation
An E proposition, the universal negative, excludes the subject class from the whole of the predicate class, so both terms are distributed. Affirmative propositions leave the predicate undistributed, and particular propositions leave the subject undistributed.
Question 40Terms, Propositions and Classification of Propositions
What is a compound proposition?
- A proposition that contains more than one adjective
- A proposition whose subject is a compound word
- A proposition that cannot be analysed into subject and predicate
- A proposition formed by combining two or more propositions with a logical connective Correct answer.
Explanation
A compound (molecular) proposition is built from simpler propositions joined by connectives such as 'and', 'or', 'if...then', or 'if and only if'. Its truth depends on the truth values of its components.
Question 41Terms, Propositions and Classification of Propositions
The proposition 'If it rains, then the ground becomes wet' is best classified as which kind of compound proposition?
- Categorical
- Disjunctive
- Conjunctive
- Conditional Correct answer.
Explanation
The form 'if...then...' expresses a conditional, in which the antecedent states a condition for the consequent. Conjunction uses 'and', disjunction uses 'or', and a categorical proposition has no such connective.
Question 42Terms, Propositions and Classification of Propositions
Which of the following propositions is modal in character?
- No triangles are circles.
- Some triangles are scalene.
- It is necessary that all triangles have three sides. Correct answer.
- All triangles have three sides.
Explanation
A modal proposition qualifies the mode in which a proposition holds, using notions such as necessity, possibility, or impossibility. The other options are plain categorical propositions without such qualification.
Question 43Terms, Propositions and Classification of Propositions
How does a hypothetical proposition differ from a categorical proposition?
- A hypothetical proposition cannot be true or false
- A hypothetical proposition asserts a relation of dependence between clauses rather than a direct subject-predicate relation Correct answer.
- A hypothetical proposition contains no terms at all
- A hypothetical proposition always has a singular subject
Explanation
A hypothetical proposition, such as a conditional, states that one proposition holds on condition of another, so its parts are propositions rather than terms. A categorical proposition instead relates two terms directly.
Question 44Terms, Propositions and Classification of Propositions
Consider the proposition 'Only citizens may vote'. How is this proposition best analysed in terms of subject and predicate?
- All citizens are voters
- No citizens are voters
- All voters are citizens Correct answer.
- Some voters are not citizens
Explanation
The word 'only' before a term signals that the term is the predicate of an affirmative universal, so 'Only citizens may vote' means 'All voters are citizens'. Misreading 'only' as a simple quantifier reverses the relation and produces the wrong paraphrase.
Question 45Terms, Propositions and Classification of Propositions
The sentence 'All that glitters is not gold' is logically ambiguous. Which reading corresponds to the O proposition form?
- No glittering things are gold
- Some glittering things are gold
- Some glittering things are not gold Correct answer.
- All glittering things are gold
Explanation
The proverb can be read as 'Not all that glitters is gold', which denies the predicate of part of the class and so has the O form. The other reading treats it as a universal negative, which is a different proposition altogether.
Question 46Terms, Propositions and Classification of Propositions
Two propositions are said to be contradictories when they satisfy which condition?
- They have the same subject and predicate but differ only in quality
- They have the same subject and predicate but differ only in quantity
- They have the same subject and predicate but differ in both quantity and quality Correct answer.
- They have entirely different subjects and predicates
Explanation
Contradictories, such as A and O or E and I, share their terms yet differ in both quantity and quality, so exactly one of the pair must be true. Differing in only one respect yields a different opposition relation.
Question 47Terms, Propositions and Classification of Propositions
A student claims that 'Some dogs are mammals' and 'Some dogs are not mammals' are contradictories. What is the precise error?
- They are subalterns, so one implies the other
- They are contraries, so both cannot be true
- They are subcontraries, so both can be true together and both cannot be false together Correct answer.
- They are not related at all because their predicates differ
Explanation
Two particular propositions with the same terms but opposite quality are subcontraries, not contradictories. Subcontraries may both be true, though they cannot both be false, so the student has misidentified the opposition relation.
Question 48Terms, Propositions and Classification of Propositions
Which pair of propositions stands in the relation of subalternation?
- 'No roses are flowers' and 'All roses are flowers'
- 'All roses are flowers' and 'Some roses are flowers' Correct answer.
- 'All roses are flowers' and 'Some roses are not flowers'
- 'Some roses are flowers' and 'Some roses are not flowers'
Explanation
Subalternation holds between a universal proposition and its corresponding particular of the same quality, so the A and I pair illustrates it. The universal implies the particular but not conversely.
Question 49Categorical Propositions, Distribution and Immediate Inference
In classical Aristotelian logic, what does it mean to say that a term is distributed in a categorical proposition?
- The term is used ambiguously in two different senses within the same proposition
- The term appears as the predicate of a proposition with universal quantity
- The term is taken in its full extension, referring to every member of the class it denotes Correct answer.
- The term names a class that is known to have at least one existing member
Explanation
Distribution concerns extension: a term is distributed when the proposition says something about the whole class the term denotes, so the term is taken universally. It is a property of how a term is used in a proposition, not of whether the class happens to be empty or non-empty.
Question 50Categorical Propositions, Distribution and Immediate Inference
Which terms are distributed in the proposition "No reptiles are warm-blooded animals"?
- Only the subject
- Neither the subject nor the predicate
- Both the subject and the predicate Correct answer.
- Only the predicate
Explanation
An E proposition excludes the subject class wholly from the predicate class, so it says something about all reptiles and about all warm-blooded animals. Hence in E propositions both terms are distributed.