Question: 1. Let A = {2k | k ∈ Z},B = {3k+1 | k ∈ Z}, and C = {6k+5 | k ∈ Z}. Show that {A,B,C} is not a partition of Z.
2. Prove the binomial theorem by induction.
3. Prove that if A ⊆ B, then A ∪ (B \ A) = B. Use element notation in your proof.
4. Encipher graph theory is the bomb using a Vigen`ere cipher with key word bat.
5. Write an algorithm that sums the first n squares.