I am supposed to write a "formal" proof for this problem and give a defense of my proof over adobe connect. Can anybody help me figure out this problem, I am not very good at proofs. Also what does a formal proof look like?

11. Suppose a and b ? Z.

a. Prove that a2 + b2 is divisible by 4 iff a and b are both even.

b. Show that it is false that a2 + b2 divisible by 8 iff a and b are both even.

.nl Verizon LTE 10:32 AM 9' 90% (:1) B snhu.brightspace.com 7. 8. 9. Suppose A, B, and C are sets. Prove that A A B E C iffA U C = B U C. Suppose A, B, and C are sets. Prove that C E A A Biff C E A U B and A n B n C =9. Suppose A, B, C, and D are sets. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. Southern New Hampsh: Univer: a. Prove that A x (B U C) = (A x B) U (A x C). b. Show that it is false that (A U B) x (C U D) = (A x C) U (B x D). . Suppose A, B, and C are nonempty sets and (A x B) E (B x C). Prove that A E B E C. . Suppose a and b e Z. a. Prove that a2 + b2 is divisible by 4 iff a and b are both even. b. Show that it is false that a2 + b2 divisible by 8 iffa and b are both even; Suppose n e N. Prove that there exists a e Z such that n2 = 8a + 1 iff n is odd. Suppose n e Z. a. Prove that n'l is divisible by 3 iff n is divisible by 3. b. Show that it is false that n2 is divisible by 12 iff n is divisible by 12. Suppose n e Z. a. Prove that (n+1)3 n3 1 is divisible by 6 for every n. b. Show that it is false that (n+1)3 n3 1 is divisible by 12 for every n. Suppose n e Z. a. Prove that if n is odd, then n3 n is divisible by 8. b. Show that it is false that n3 n is divisible by 8 for every n. Consider the function f(x) = 1/x for x e R and 1