Decide which statement is true and which is false, and give proof/disproof of both. 1.Let n be any integer. Prove by cases that n3 − n is evenly divisible by 3. 2.Let n be any integer. Prove by cases...

Decide which statement is true and which is false, and give proof/disproof of both.

1.Let n be any integer. Prove by cases that n3 − n is evenly divisible by 3.

2.Let n be any integer. Prove by cases that n2 + 1 is not evenly divisible by 3.

3.Prove that |x| + |y| ≥ |x + y| for any real numbers x and y.

4. Prove that |x| − |y| ≤ |x − y| for any real numbers x and y.

5. Prove that the product of the absolute values of x and y is equal to the absolute value of their