**Problem 1**. Exercises 8 and 10 from Section 2.5

**Problem 2**. What are “DeMorgan’s Laws?”

**Problem 3**. Exercises 9 and 10 from Section 2.6

**Problem 4**. Exercises 4, 5, and 8 from Section 2.7

**Problem 5**. Exercises 4, 10, and 11 from Section 2.10

**Problem 6**. Describe at least two facts that our textbook explicitly claims we will accept without proof or justification.

**Problem 7**. Let. Prove that . (Be sure you are only using the definition of *least common multiple**.*)

**Problem 8**. Here is a proof of *some* statement. Read it, and then write down the claim that was proved.

*proof*. Let be arbitrary. If so that , then is even. Suppose, then, that is *not* even. This means that for all integers . By the Division Algorithm, there exists so that where . This implies that either or . However, if , then we have , which is impossible since we have assumed is not even. Therefore and we have that . This implies that is odd, completing the proof. .

**Problem 9**. Prove that if and if then .

**Problem 10**. Prove that if , then .

**Problem 11.** Exercises 4, 8, 14, and 26 from Chapter 4 exercises.