u/Gauss34

I’m reading an example from Velleman’s proof book where he proves both directions of the biconditional statement (x is even) iff (x\^2 is even).

For the forward direction, (x is even) implies (x\^2 is even), he assumes the antecedent as usual.

For the converse, (x\^2 is even) implies (x is even), he proves the contrapositive.

What is it about some of these proof problems that forces you to prove the contrapositive form of a conditional statement, instead of just the typical form?

I’m reading an example from Velleman’s proof book where he proves both directions of the biconditional statement (x is even) iff (x^2 is even).

For the forward direction, (x is even) implies (x^2 is even), he assumes the antecedent as usual.

For the converse, (x^2 is even) implies (x is even), he proves the contrapositive.

What is it about some of these proof problems that forces you to prove the contrapositive form of a conditional statement, instead of just the typical form?