Proof). study the following claim as well as the "proof" problem 4.5 (grade a claim. for all sets a, b, c and d, (ax b)- (cx d) (a- c) x (b- d). "proof". let a. b, c and d be sets. let (x, y) (ax b) - (c (z, y) ax b and (z. y) cx d. thus r a, z c. y eb and y d. in other words, z e a-c and y eb-d; hence (r. y) since every element in (a x b) -(c x d) is in (a - c) x (b- d), (ax b) -(c x d) (a - c) x (b - d). this completes the proof. d), so that x e (a- c) x (b - d). we conclude complete the following questions concerning the above claim and "proof" (1) determine whether the "proof" is rigorous. identify the issues in the "proof", if any (2) determine whether the claim is true or false. justify the answer in part (3). (3) if the the claim is true and the "proof" is not rigorous, then provide a correct and rigorous proof. if the claim is false, give a concrete counterexample. hint. complete the parts as instructed. if the claim is false, then (obviously) there is no way the "proof" could be correct.