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Spec: PRF2 · No calculator · ~200s
Letters only — the answer key is hidden. Work it out, then check the solution below.
No written hint yet — check the trope: even-odd-split-missing. Name the trap first, work the stem by hand, then open the solution below.
Same topic · same level
TMUA-P2-PRF2-003
Prove: for every integer n, the remainder of n^2 on division by 4 is 0 or 1. Which case argument is valid?
Proof by cases
Same trap: even-odd-split-missing
TMUA-P2-ERR1-007
A student “proves” n^2 + n is odd for every integer n: “If n is even, n = 2k, so n^2 + n = 4k^2 + 2k = 2(2k^2 + k), whic…
Identifying errors in proofs
Step up a level
TMUA-P2-PRF2-006
A lecturer proves that n^3 - n is divisible by 3 for every integer n by splitting into remainders modulo 3, writing n =…
Proof by cases