Question: Please do all even numbers B. Prove the following statements using either direct or contrapositive proof. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Please do all even numbers

B. Prove the following statements using either direct or contrapositive proof. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. If a,b e Z and a and b have the same parity, then 3a + 7 and 7b 4 do not. Suppose x E Z. If x3 1 is even, then x is odd. Suppose x, y e Z. If x + y is even, then x and y have the same parity. If n is odd, then 8 | (n2 1). If a, b e 2, then (a + b)3 a a3 + b3 (mod 3). Let a,b,c e Z and n e N. Ifa E b (mod n) and a E c (mod n), then c E b (mod n). Ifa e Z and a E 1 (mod 5), then a2 E 1 (mod 5). Let a,b E Z and n e N. Ifa E b (mod n), then a3 E b3 (mod n). Let a e Z, n e N. If a has remainder r When divided by n, then a E r (mod n). Let a,b E Z and n e N. Ifa E b (mod n), then a2 E ab (mod n). Ifa E b (mod n) and c E d (mod n), then ac 5 bd (mod n). Let n e N. If 2\" 1 is prime, then n is prime. If n = 2k 1 for k e N, then every entry in Row n of Pascal's Triangle is odd
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