Exercise · ZW-PROOF-BY-CONTRADICTION-010 · ★★★ Advanced
We want to prove that among any three integers two have the same parity. Assume not. What is the contradiction?
Choose one option.
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- C. Three integers would need three pairwise different parities, but only two exist
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Explanation
If all parities were different, three integers would need three different parities, but only two exist: even and odd.
A proof by contradiction of a statement \(p\) assumes \(p\) is false and deduces something absurd from it, so that \(p\) must be true.
\[\neg p\Rightarrow(r\wedge\neg r)\ \therefore\ p\]
More practice problems: proof by contradiction