Question 3 (4 pts). Show that 11k+2 + 6k + 10k 7 is divisible by 5 for any k N with a proof by induction.

For the proof of Question 4, you are not required to justify the steps associated to the Chapter 1 material.

tion by its number in the s specific proof constraints that you should follow to the letter. QUESTION 1 (4 pts). Suppose x, y, z, w E Z. Show that (yz - I)w + w = (wz)y - (IW -w). For the proof of Question 1 above, you are allowed to use any axioms and propositions from Sections 1.1 and 1.2, and the definition of subtraction. You are NOT allowed to use propositions from Section 1.3. QUESTION 2 (5 pts). (i) [Proposition 2.13; Exercice 2.2.5] Show that, for any a, b E Z, the following implication holds: [a E N and ab EN - bEN Indication: Use Proposition 2.10 to consider three cases: b 0. (2 points) For the proof of (i) above, you are allowed to use any axioms and propositions up to Proposition 2.12 in the Official Course Notes. Also, you are not required to justify the steps associated to the Chapter 1 material. (ii) Let m, n E Z. Show that, if m2 2 n2 and m - n EN, then m + n 2 0. (3 points) For the proof of (2i) above, you are ONLY allowed to use the definition of