A student proves "if n² is even then n is even" by assuming n is odd, writing n = 2k+1, and deriving that n² is odd. Which technique is this, and is the proof finished?

Question

Accepted Answer

Contrapositive, and it is finished, since the two are logically equivalent.

Answer

Contrapositive, but unfinished, the converse "n even ⇒ n² even" still has to be shown.

Answer

Contradiction, and it is unfinished, because no absurdity was ever reached.

Answer

A direct proof, and it is finished, because it starts from the definition of an odd number.

A student proves "if $n^{2}$ is even then $n$ is even" by assuming $n$ is odd, writing $n = 2k+1$ , and deriving that $n^{2}$ is odd. Which technique is this, and is the proof finished?

Practise Proof Techniques

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A student proves "if n2n^{2}n2 is even then nnn is even" by assuming nnn is odd, writing n=2k+1n = 2k+1n=2k+1, and deriving that n2n^{2}n2 is odd. Which technique is this, and is the proof finished?

Practise Proof Techniques

More questions on Proof Techniques

A student proves "if $n^{2}$ is even then $n$ is even" by assuming $n$ is odd, writing $n = 2k+1$ , and deriving that $n^{2}$ is odd. Which technique is this, and is the proof finished?