Practice question · Multiple choice
Proof by contrapositive and proof by contradiction both begin by assuming a negation. What distinguishes them, and why is the contrapositive usually preferred where both apply?
Hints
- Write down what each proof assumes at its first line. How many assumptions?
- One of them ends by deriving a specific conclusion; the other ends by deriving anything absurd.
Show the answer
D. Contrapositive assumes ¬q and derives ¬p; contradiction assumes both.
Why
A contrapositive proof carries one assumption and works toward a named target; a contradiction proof carries two and hunts for any absurdity at all. Contradiction earns its place where there is no implication to contrapose, the irrationality of √2 being the standard case, since there is no q to negate.
Practise Proof by Contradiction and Contrapositive
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More questions on Proof by Contradiction and Contrapositive
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