Logical and Analytical Reasoning
What to master
Deductive validity (if–then reasoning, contrapositives), syllogisms, necessary versus sufficient conditions, ordering and grouping puzzles, and spotting assumptions and flaws in arguments.
Traps that appear
- Affirming the consequent: from "If P then Q" and "Q," you cannot conclude "P." Only the contrapositive (not Q → not P) is valid.
- Confusing necessary and sufficient: "All doctors studied biology" does not mean "all who studied biology are doctors."
- Reversing a relationship: "A is taller than B" does not imply "B is taller than A"; track direction carefully.
- Ignoring "some" vs "all": "Some X are Y" tells you nothing about whether other X are not Y.
- Extra constraints in puzzles: missing a "must be together" or "cannot be adjacent" rule derails the whole arrangement.
Rule of thumb
For conditionals, write the rule and its contrapositive side by side. For puzzles, build a compact grid or list of the fixed rules first, then test each option against every rule; the first rule an option violates eliminates it.
Worked example
"If it rains, the match is cancelled. The match was cancelled." This does not prove it rained - other causes exist. But "the match was not cancelled" does prove it did not rain (contrapositive).