a) Explain what it means for two sets to be equal.________________b) Describe as many of the ways as you can to show that two sets are equal.________________c) Show in at least two different ways that the sets. A ? (B?C) and (A ? B) ? (A ? C) arc equal.

Solution:Step1a) we have to explain what it means for two sets to be equal.Two sets to be equal means both of sets having same number of elements.Therefore, sets C and D are equal if y[y C y D]. Expressed as C=D.ExampleIf C= {2, 4, 6, 8, 10}And, D = {10, 12, 18, 20, 22}Then, n(C)= n(D)= 5, this means sets C and D are equal.Step2b) we have to describe the ways as you can to show that two sets are equal.The ways to show that two sets are equal:-Assume that C and D are sets the C and D are equal if and only if Assume that C and D are sets the C and D are equal if and only if Step3c) We have to show at least two different ways that the sets. A (BC) and (A B) (A C) are equal.Two different ways that the sets. A (BC) and (A B) (A C) are equal:-1. By algebraic method = = =Therefore, by algebraic method A (BC) and (A B) (A C) are equal.2. By identity methodLet It is clear thatThis means A (BC) and (A B) (A C) are equal.