Solution for Section 5.1 Question 6

6. Proof We must show that A Í  B and that B Í  A.

Assume xÎ A. Then x = 4p - 1 for some integer p.
Thus x = 4p - 1 = 4(p+1) - 4 - 1 = 4(p+1) - 5, where p+1Î Z. Hence x Î B and  A Í  B.

Assume y Î B. Then y = 4q - 5 for some integer q.
Thus y = 4q - 5 = 4(q - 1) - 1, where q - 1 Î Z. Hence y Î A and  B Í A.

Thus we may deduce that A = B.

Back to Section 5.1