.For this question, you will prove the following set identity in two ways: Qla. using a membership table with a brief explanation 3 points Q1b. using the Laws from the Table of Important Set Identities. 4 points You may use one or two laws at each step, and you must write the name of the law(s) used at each step. Do not combine more than two laws in one step. Do not omit necessary parentheses. Screenshot Q2. Let f : R R R R be the function given by the rule f(g, r)-(5q + r, q Q2a. Prove that f r). is injective (ie. one-to-one). 3 points Q2b. Prove that f is surjective (i.e. onto) 3 points Screenshot . [5 points] Let A and B denote arbitrary finite sets. For each of the following two claims, determine whether it is always true (no matter what the finite sets are) or sometimes false (for certain particular sets). If you circle always true, then you must give a detailed proof. If you circle sometimes false, then you must give a counterexample, that is, give a concrete pair of finite sets A and B (list their elements) and briefly explain how the sets you gave demonstrate that the claim can be false. Claim 3a. A-Bl = IAI-BI. Circle always tru sometimes false Claim 3b. If (A - B)C (B - A), then AC B. Circle always true sometimes false Screenshot (BONUS) [+2 bonus points] Circle the best answer for each question. You do not need to show any justification for this, but you will only earn the bonus points if all of your answers are correct. i. For any sets A and B, is the following claim always true, or can it sometimes be false? Claim: If A C B, then (A - B)C (B - A). ii. Let h : R R x Z-+ R x R be the function given by h(g, r, k)-(5q + r, q-r + k). Circle always true sometimes false Is h injective? Is h surjective? Circle: yes no Circle: yes no 4 Screenshot