1. Use the contradiction proof method to prove that if a not divisible b and a | c, then a not divisible b + c,for any integers a, b, and c.

2. Use the contrapositive proof method to prove that if a, b, c, and d are integers where ab not divisible cd, then a not divisible c or b not divisible d.

3. Use the cases proof method to prove that for any integer a, at least one of the integers a, a + 2, and a + 4 is divisible by 3. (Hint: a must have a remainder of 0, 1, or 2 when divided by 3.)