1) Use a direct proof to show that the sum of three odd numbers is always odd. Hint: Express the three odd numbers as 2j+1, 2k+1 and 2m+1 where j, k and m are integers.

2) Use a proof by cases to show that every perfect square is an odd number or else a multiple of 4. Hint: Use four cases: n= 4k, n= 4k+1, n = 4k+2, n = 4k+3.

3) Use a proof by contraposition to show for any integer n: "If n2 is even , then n is even."

4) Use a proof by contradiction to show that the square root of 98 is irrational. Do not try to replicate the proof that the square root of 2 is irrational, instead, you should use the fact that the square root of 2 is irrational as part of your proof.