Contrapositive proof
Claim: if n^2 is even, n is even. Contrapositive: if n is odd, n=2k+1, then n^2=4k^2+4k+1 is odd.
- A statement and its contrapositive are equivalent.
- Trace the worked reasoning before selecting the conclusion.
definitions, logic, counterexample, rigor, and exposition
Claim: if n^2 is even, n is even. Contrapositive: if n is odd, n=2k+1, then n^2=4k^2+4k+1 is odd.
Pause. Find what matters. Then make your move.