Prove the following discrete math questions and indicate which proof

3. Prove each of the following. Be sure to indicate whether you are using a Direct Proof, a Contrapositive Proof, a Constructive Proof, or a Proof by Contradiction. (a) Suppose n is an integer. Prove that n2+4n +5 is odd if and only if n is even. (b) Prove that if 3 divides 4-1 -1, then 3 divides 4 -1. Hint: 3 divides a number N if you can write N as N = 3k where k is an integer. (c) Suppose you have two empty jugs with volumes of 7 gallons and 11 gallons. You can assume that you have access to an unlimited water source, and that you measure out the requested amounts of water by successively filling and pouring water from one jug into the other or down the drain. Prove or disprove that an algorithm exists to put exactly 10 gallons of water in the 11 gallon jug