please help 1 Prove using contraposition that for all intege

please help

1-  Prove using contraposition that for all integers m and n, if mn is even, then m is even or n is even.

2-  Prove that for all integers a, b, c, s, and t, if a|b and a|c, then a|(sb ? tc).

3-  Prove that for any even integer m and odd integer n that 3m + 5n is odd.

Solution

1. If both m an dn are odd then the product of odd and odd is always odd. So either m or n is even or both is even.

3. If m is even then 3m is also even. If n is odd then 5n is always odd because product of odd is always odd.

If we add even and odd we always get odd.