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Let P and Q be two finite sets such that n(P-Q)=20,n(P union Q)=95.n(PintersectionQ)=35, then n(Q-P) IS ?

Asked by Sunil Kumar P 13th October 2014, 8:29 PM
Answered by Expert
Answer:
W e space k n o w space t h a t comma space n open parentheses P minus Q close parentheses equals n open parentheses P close parentheses minus n open parentheses P intersection Q close parentheses... left parenthesis 1 right parenthesis G i v e n space t h a t space n open parentheses P minus Q close parentheses equals 20 comma space n open parentheses P union Q close parentheses equals 95 space a n d space n open parentheses P intersection Q close parentheses equals 35 U sin g space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma rightwards double arrow space 20 equals n open parentheses P close parentheses minus 35 rightwards double arrow n open parentheses P close parentheses equals 55 A l s o comma space w e space k n o w space t h a t comma space n open parentheses P union Q close parentheses equals n open parentheses P close parentheses plus n open parentheses Q close parentheses minus n open parentheses P intersection Q close parentheses.... left parenthesis 2 right parenthesis T h u s comma space w e space space h a v e comma 95 equals 55 plus n open parentheses Q close parentheses minus 35 rightwards double arrow 95 equals 20 plus n open parentheses Q close parentheses rightwards double arrow n open parentheses Q close parentheses equals 95 minus 20 rightwards double arrow n open parentheses Q close parentheses equals 75 A g a i n space u sin g space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma n open parentheses Q minus P close parentheses equals n open parentheses Q close parentheses minus n open parentheses P intersection Q close parentheses rightwards double arrow n open parentheses Q minus P close parentheses equals 75 minus 35 rightwards double arrow n open parentheses Q minus P close parentheses equals 40
Answered by Expert 14th October 2014, 9:13 AM
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