Please show the step by step answer below(question 5),this is not assignment question.

the event b is impossible if and only if for every event A. A = (BnA' ) U ( Ben A ). 4. Cards In an experiment, cards are drawn, one by one, at random and successively from an ordinary deck of 52 cards. Let An be the event that no face card or ace appears on the first n - 1 draws, and the nth draw is an ace. In terms of Ans, find an expression for the event that an ace appears before a face card, if (a) the cards are drawn with replacement; (b) they are drawn without replacement. 5. Event Identities Let A and B be two events. Prove the following relations by the elementwise method. (a) (A\\ (An B)) UB = AUB; ( b) ( AUB) \\ ( AnB) = (An Bo ) U ( AnB ). 6. Infinite Sequence of Sets Let { A1, A2, A3, . . .} be a sequence of events of a sample space S. Find a sequence { B1, B2, B3, . . .} of mutually exclusive events such that for all n 2 1, Un , Ai = Un_Bi