1. Let x ∈ Z. Use a direct proof to show that if 5x 2 + 8 is odd then x is odd. 2. Show by contraposition that for positive real numbers a and b, if ab − a − b ≥ 0 then a and b are both more than 1....

1. Let x ∈ Z. Use a
direct proof to show that if 5x² + 8 is odd then x is odd.

2. Show
by contrapositionthat for positive real numbers a and b, if ab − a − b ≥ 0 then a and b are both more than 1.

3. Prove
by contradiction that if m and n are integers, then m²- n²  is even or
m + nis odd