Paper 2 logic starts with the conditional 'If P then Q': P is the hypothesis, Q the conclusion, and the whole claim is false in exactly one circumstance — P true with Q false. When the hypothesis fails the implication is vacuously true, a fact examiners probe directly. The inclusive 'or' of mathematics works with the same precision: 'P or Q' is false only when both parts are false, never in the everyday either/or sense. Translate every option into symbols before comparing — words like 'unless' and 'only if' are designed to be misread under time pressure.
Three variants orbit every conditional. The converse swaps the parts ('If Q then P') and is not equivalent to the original: 'divisible by 6 implies divisible by 3' is true, but n = 9 kills its converse. The contrapositive negates and swaps ('If not Q then not P') and is always equivalent — 'rain implies cancellation' stands or falls with 'match on, so no rain'. The claim 'P if and only if Q' asserts both directions at once, so proving one arrow and declaring victory is the signature half-proof error.
Method: for equivalence questions, hunt the contrapositive first — it is the correct answer more often than any other single form. For 'only if' claims ('prime above 2 only if odd'), rewrite as a forward arrow immediately. Distractors serve the converse, the inverse, or a scope-shifted restatement of the evidence; each dies the moment you write P and Q explicitly and test the single true/false row that matters. Finally, budget one full pass that only translates — no solving — because every ARG1 miss in review traces back to an arrow drawn backwards in the first thirty seconds.
Study method: attempt five timed questions, log every miss with its topic code, redo misses from scratch within 48 hours, then re-attempt the topic a week later. Pair each hub with its drill link below and a fortnightly full mock.
Place this topic in the wider test with the syllabus checklist and Paper 1 vs Paper 2, learn the timing system in how to prepare, and check what scores mean in scores explained.