TMUA-P2-PRF1-002 — Paper P2 · Direct proof · Level 1

Options

1. A
   Take odd $m = 2j + 1$ and odd $n = 2k + 1$; then $m + n = 2(j + k + 1)$, which is even.
2. B
   Take $m + n = 2t$; then $m$ and $n$ must both be odd.
3. C
   Check $1 + 3 = 4$; one example proves it.
4. D
   Assume $m + n$ is odd and derive a contradiction.
5. E
   Take $m = 2j$, $n = 2k$; then $m + n = 2(j + k)$.

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

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