Karnataka II PUC Logic (KSEAB) common mistakes
Karnataka II PUC Logic (KSEAB) · Understand the traps and how to avoid them.
Writing that logic studies the 'art of winning arguments' or 'thinking correctly in general', and treating logic as a branch of psychology because it describes how people actually reason.
Students absorb the popular meaning of 'logic' from debate clubs and everyday speech, and textbooks' opening definitions ('science of the laws of thought') get misread as a claim about mental processes. The distinction between a normative science of correct inference and a descriptive science of actual thinking is stated once in Chapter 1 and never revisited.
What to do instead
Memorise the working definition as 'the science of the necessary conditions of valid inference' and drill the contrast: psychology describes how we do think; logic prescribes how we must think if our conclusions are to follow. For each of the pair 'normative/descriptive', 'formal/material', write one exam-ready sentence you can reproduce under time pressure.
Confusing 'term' with 'word', or claiming a term is always a single word, so that 'the President of India' is denied the status of a term while 'university' is accepted as one.
School grammar teaches that words are the units of language, and the logical definition (a term is a word or group of words that can be the subject or predicate of a proposition) is memorised without the test being applied. Students also forget that a term must be capable of standing alone as subject or predicate.
What to do instead
Apply the substitution test every time: place the expression before or after 'is' in a sentence and ask whether it functions as subject or predicate. Practise with multi-word terms ('the tallest building in Bengaluru') and with syncategorematic words ('and', 'if', 'very') that fail the test. State explicitly in answers that a term may be a single word or a group of words.
Classifying a sentence by its grammatical form rather than its logical form - labelling 'All that glitters is not gold' as A, or 'Only graduates may apply' as A because it looks affirmative.
Examiners deliberately use sentences whose grammatical structure misleads: 'only', 'few', 'all…not', and rhetorical questions. Students classify by the presence of 'all' or by the verb, without reducing the sentence to standard subject-copula-predicate form first.
What to do instead
Always rewrite into strict standard form before classifying. 'Only graduates may apply' becomes 'All who may apply are graduates' (A). 'All that glitters is not gold' becomes 'No things that glitter are gold' (E). 'Few politicians are honest' becomes 'Some politicians are not honest' (O). Keep a personal list of these translation traps and re-derive each one from the meaning, not the wording.
Treating distribution as a property of the term's meaning or of the proposition's quality alone - for example saying the predicate of an A proposition is distributed because A is universal.
The distribution rules are four short rows in a table and are memorised as a chant (A: subject only; E: both; I: neither; O: predicate only) without the underlying test: does the proposition say something about every member of the class denoted by the term? Quality and quantity are conflated because both appear in the same table.
What to do instead
For every term, ask the single question: 'If this proposition is true, is it thereby settled for every member of this class?' Verify each row by counterexample - 'All dogs are animals' says nothing about every animal, so the predicate of A is undistributed. Write the distribution column beside every proposition you symbolise for a week, then check yourself against the table rather than reciting it.
Converting an A proposition by simple conversion ('All cats are mammals' therefore 'All mammals are cats') or obverting incorrectly by changing both quality and predicate.
Conversion, obversion and contraposition all transform the same proposition, and students apply the mechanics of one to another. The rule that A converts only by limitation (per accidens) is easy to forget because E and I convert simply, and obversion's requirement to change the quality while negating the predicate is dropped under exam pressure.
What to do instead
Learn each operation with its own invariant: conversion swaps terms and must preserve truth, so A converts to I; obversion changes quality and negates the predicate, leaving quantity and truth-value untouched; contraposition replaces subject and predicate by their complements and is valid for A and O. Test every answer by asking whether the original could be true while your result is false - if yes, the inference is invalid.
Declaring a categorical syllogism valid because the conclusion is true, or invalid because the conclusion is false, and failing to identify the middle term before applying the rules.
Everyday reasoning rewards true conclusions, and students carry that habit into formal logic. Under time pressure they also mistake the predicate of the conclusion for the middle term, which corrupts all subsequent rule checks (undistributed middle, illicit major, illicit minor).
What to do instead
Adopt a fixed procedure and write it out in the answer: (1) locate the conclusion, (2) label its subject S and predicate P, (3) the remaining term is M, (4) write the mood and figure, (5) test against the five rules in order. Practise on syllogisms with true conclusions and invalid form so the habit of separating truth from validity is broken early.
Mixing up the four figures, or giving the fallacy name without showing which rule it violates - writing 'fallacy of undistributed middle' as a bare label with no term analysis.
Figure depends on the position of the middle term in the premises, and students memorise moods (Barbara, Celarent) without the positional diagram. Marking schemes award steps, so a bare label loses most of the marks even when the label is right.
What to do instead
Draw the figure as a small diagram every time: M–P/P–M etc., with S and P fixed in the conclusion. Then state the violation explicitly, e.g. 'M is undistributed in both premises, so the syllogism commits the fallacy of undistributed middle'. Answer in numbered steps so partial credit is visible to the examiner.
Confusing the converse, inverse and contrapositive of a conditional, or treating 'p ⊃ q' as equivalent to 'q ⊃ p', and misreading 'unless' and 'only if'.
The truth table for the conditional feels counter-intuitive (false only when the antecedent is true and the consequent false), so students fall back on the conversational implication that the antecedent causes the consequent. 'Unless' and 'only if' are translated from ordinary speech rather than from their logical equivalents.
What to do instead
Memorise the equivalences as a set: p ⊃ q ≡ ~q ⊃ ~p ≡ ~p ∨ q. Translate 'p unless q' as ~q ⊃ p, and 'p only if q' as p ⊃ q. For every translation, construct a one-line truth table or a counterexample sentence to confirm it before moving on.
Producing a truth table with the wrong number of rows, or stopping the indirect proof (reductio) after deriving a contradiction without stating what the contradiction shows.
Row count depends on the number of distinct propositional variables (2ⁿ), and students count atomic letters including repeats or forget to count at all. In indirect proof the aim is to show the negation of the conclusion is inconsistent with the premises, and the final step - 'therefore the original conclusion is established' - is routinely omitted.
What to do instead
Before drawing any table, list the distinct variables and write '2ⁿ = …' explicitly. For indirect proof, open by writing the negation of the conclusion as an assumed premise, derive a contradiction in the form 'A · ~A', and close with the sentence 'Since the assumption leads to a contradiction, the conclusion is proved'. Do three full worked examples of each method from scratch without looking at the textbook.
Calling an enumerative generalisation a perfect induction, or describing Mill's method of difference as 'comparing two similar cases' without identifying the single varying circumstance.
Induction topics are taught late in the syllabus and often skimmed, so the distinctions between perfect induction, ordinary induction and analogy collapse into 'going from particular to general'. Mill's methods are memorised by name without the controlled-comparison idea behind each.
What to do instead
Write a one-line definition for each with a concrete Indian example: perfect induction covers all members ('all seven days of the week have 24 hours'); enumerative induction generalises beyond observed cases; analogy transfers a property on the basis of resemblance. For Mill, learn the question each method answers - agreement: what is common to cases where the effect occurs; difference: what is present when it occurs and absent when it does not.
Dismissing every emotive or figurative sentence as meaningless, or labelling any persuasive writing as the fallacy of equivocation, without distinguishing the cognitive from the emotive use of language.
The chapter on language and logic introduces the cognitive/emotive distinction and the informal fallacies together, and students over-apply the vocabulary. They also miss that a word can shift meaning within one argument (equivocation) even when the argument is otherwise well formed.
What to do instead
For each passage, first ask whether it asserts something capable of being true or false; if it does, it has cognitive content even if emotive too. Reserve 'equivocation' for cases where the same word carries two different senses in the premises, and quote both occurrences to prove it. Practise on short newspaper passages, labelling each sentence cognitive, emotive, or both.