can you help me explain all problem?

5. Choose THREE of the following to prove or disprove. Write your choice on the line. You may not do extra for bonus here. You must use full sentences to receive full credit. You will likely use some equations. Just be sure to connect everything with sentences. (10 points each) (a) If m is the sum of any four consecutive positive integers, then m mod 4 = 2. (b) For all rational numbers a and b, a is rational. (c) For all integers n , if n mod 5 = 1 then n2 - n mod 5 = 0. (d) 3(n3 - n) for every positive integer n. Option 1:6. Prove TWO of the following statements using induction. Write your choice on the line. You may not do extra for bonus here. You must use full sentences to receive full credit. You will likely use some equations. Just be sure to connect everything with sentences. (10 points each) a ) an = 17 ( 3 n ) is a solution to the recurrence relation an = 3an-1 + 7 with ao = 5 for n 2 1. b) 34n+2 + 52n+ is divisible by 14 for all integers n 2 0 C) 6 + 8 + 10 + ... + (2n +4) = n2 + 5n for all n 2 1 Option 1