Prove the following claims using a proof by contrapositive. 1.Let n ∈ Z≥0 . If n mod 4 ∈ {2, 3}, then n is not a perfect square. 2. Let n and m be integers. If nm is not evenly divisible by 3, then...

Prove the following claims using a proof by contrapositive.

1.Let n ∈ Z≥0 . If n mod 4 ∈ {2, 3}, then n is not a perfect square.

2. Let n and m be integers. If nm is not evenly divisible by 3, then neither n nor m is evenly divisible by 3. (In fact, the converse is true too, but you don’t have to prove it.)

3. Let n ∈ Z≥0 . If 2n 4 + n + 5 is odd, then n is even.