Practice question · Multiple choice
A proof by contradiction and a proof by contrapositive both begin by assuming something false. Which is preferred for an implication, and why?
Hints
- Write the first line of each proof of 'if p then q'. Count the assumptions.
- One ends by deriving ¬p. The other ends by deriving anything false. Which gives you direction?
Show the answer
B. Contrapositive, which carries one assumption and a named target
Why
Contrapositive assumes ¬q and aims at ¬p; contradiction assumes p and ¬q and searches for any absurdity. Fewer assumptions and a specific target make the first easier to write and to read. Contradiction earns its place where there is no implication to contrapose, the irrationality of √2 being the standard case.
Practise Proof Techniques
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