Under Latex format, using discrete mathematics (Proof, base case, induction)

Required Problems 1. (10 points) Prove Li* fact(i) = fact(n+1) 1 i=0 for all n e N. Put your name, MacID, and date here. Put your solution here. 2. [10 points] Prove that, for all n N, fib(n) is even if n = 3k for some ke N, is odd if n = 3k +1 for some k N, and is odd if n = 3k + 2 for some k e N. Put your name, MacID, and date here. Put your solution here