TMUA-P2-PRF4-007 — Paper P2 · Disproof by counterexample · Level 3

Options

1. A
   $m = 2$, $n = 4$: product even, both even — so the conjecture holds.
2. B
   $m = 3$, $n = 5$: product odd, so the hypothesis fails and nothing follows.
3. C
   $m = 2$, $n = 3$: $mn = 6$ is even, yet $n = 3$ is odd, so one even factor suffices and the universal is false.
4. D
   The conjecture is true because an even product must come from even factors.
5. E
   No counterexample exists since parity always transfers to both factors.

Letters only — the answer key is hidden. Work it out, then check the solution below.

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