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Spec: PRF2 · No calculator · ~180s
Letters only — the answer key is hidden. Work it out, then check the solution below.
No written hint yet — check the trope: case-split-modulus, sign-case-omission. Name the trap first, work the stem by hand, then open the solution below.
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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: case-split-modulus
TMUA-P2-PRF2-007
To solve |x-3|=5 by cases, which split is complete and correct?
Proof by cases
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