1. Prove or give a counterexample: For all x > 0, we have x 2 + 1 2 ≤ 2(x 2 + 1). 2. Mark each statement True or False. Justify each answer. (a) If A ⊆ B and A ≠ B, then A is called a proper subset...

1. Prove or give a counterexample: For all x > 0, we have x²
+ 1 <>²
≤ 2(x²
+ 1).

2. Mark each statement True or False. Justify each answer.

(a) If A ⊆ B and A ≠ B, then A is called a proper subset of B.

(b) The symbol N is used to denote the set of all integers.

(c) A slash (/ ) through a symbol means “not.”

(d) The empty set is a subset of every set.