Using contrapositive method prove that if n2 is an even integer, then

1.	Using contrapositive method prove that if n2 is an even integer, then n is also an even integers.
Answer» Let us assume p: n² is an even integer. ~p: n is not an even integer q: n is also an even integer ~q=n is not an even integer. Since, in the contrapositive, a conditional statement is logically equivalent to its contrapositive. Therefore, ~q → ~p = If n is not an even integer then n² is not an even integer. Hence, ~q is true → ~p is true.

Using contrapositive method prove that if n2 is an even integer, then n is also an even integers.

Answer»

Let us assume

p: n² is an even integer.

~p: n is not an even integer

q: n is also an even integer

~q=n is not an even integer.

Since, in the contrapositive, a conditional statement is logically equivalent to its contrapositive.

Therefore,

~q → ~p = If n is not an even integer then n² is not an even integer.

Hence, ~q is true → ~p is true.