Analytical and Logical Reasoning
Inference types
Deduction moves from general rules to a conclusion that must follow; induction generalizes from observations and is only probable; abduction picks the best available explanation. Validity concerns structure alone; soundness requires true premises plus valid structure.
Conditionals
From “If P then Q” only two moves are valid: modus ponens (P, therefore Q) and modus tollens (not Q, therefore not P - the contrapositive). The converse (Q, therefore P) and the inverse (not P, therefore not Q) are both invalid. Distinguish necessary from sufficient conditions: “only if” introduces a necessary condition, while “if” introduces a sufficient one.
Quantifiers and sets
“All A are B” does not imply “all B are A”. “Some A are B” does imply “some B are A”. De Morgan's laws: not (A and B) = (not A) or (not B); not (A or B) = (not A) and (not B). Draw Venn diagrams before answering quantifier items.
Sequences and fallacies
For number series, check differences, ratios, alternating sub-series, squares, and primes; for letter series, convert letters to positions. Common fallacies: affirming the consequent, denying the antecedent, false dichotomy, hasty generalization, straw man, circular reasoning, appeal to authority.
Traps
“Which must be true” demands a valid deduction, not a plausible statement. Answer choices often quietly reverse a conditional or swap “some” for “all”.
Worked example
Premises: all analysts are cleared; some cleared staff are not analysts. Does “some analysts are not cleared” follow? No - the first premise forbids it. Rule of thumb: test each conditional answer against a single counterexample before choosing.