1. Prove or give a counterexample: For every positive integer n, n 2 + 3n + 8 is even. 2. Prove or give a counterexample: For every positive integer n, n 2 + 4n + 8 is even. 3. Prove or give a...

1. Prove or give a counterexample: For every positive integer n, n²
+ 3n + 8 is even.

2. Prove or give a counterexample: For every positive integer n, n²
+ 4n + 8 is even.

3. Prove or give a counterexample: There do not exist irrational numbers x and y such that x^y
is rational

4. Prove or give a counterexample: There do not exist rational numbers x and y such that x^y
is a positive integer and y^x
is a negative integer