Exercise 1. Prove that if a

Let a and b be integers such that ab and ba. Prove that b=0.

25. Prove that if and are integers and, then either or. (Hint: If, then either or, and similarly for. Consider for the various causes.)

To prove a theorem of the form "If P, then Q" by the indirect method, the first line of the proof should read: Suppose that ___________ is true.

Prove the half of Theorem 3.3 (e) that was not proved in the text.

Let and . Prove or disprove that .

Prove that if , , and , then .

If a0 and ab, then prove or disprove that (a,b)=a.

30. Prove statement of Theorem : for all integers .

Name, in order, the five parts of the formal proof of a theorem.