PAPER 2 LOGIC ACADEMY
A free structured route through the reasoning skills that repeatedly decide Paper 2 questions: necessary and sufficient conditions, contrapositives, counterexamples, quantifiers and first-error proof audits.
Write ‘A only if B’ as \(A \Rightarrow B\) and ‘A if B’ as \(B \Rightarrow \) A before doing any mathematics. This prevents a large class of Paper \(2\) errors.
After proving one direction, deliberately ask whether the reverse direction is true. If not, find the smallest clean counterexample that preserves every assumption.
For statements of the form \(A \Rightarrow B\), proving ¬B \(\Rightarrow \) ¬A can be cleaner, especially in parity and divisibility arguments.
Paper \(2\) proof-error questions reward finding the first unjustified step, not merely observing that the final claim is false. Check division by zero, sign changes, square roots, cancelled factors and hidden domain assumptions.
FREE PRACTICE
These questions now draw from the current reviewed CF Maths banks, including image and diagram items where appropriate. Open the solution only after you have committed to a route.
