Help me with these problems : 7, 8, 9, 11

7. Prove that for all integers m and n, if m and n are even, then m+n is even. 8. Prove that for all integers m and n, if m and n are odd, then m+n is even. 9. Prove that for all integers m and n, if m and n are even, then mn is even. 10. Prove that for all integers m and n, if m and n are odd, then mn is odd. 11. Prove that for all integers m and n, if m is odd and n is even, then mn is even