116744 If the sets A and B are as follows: A={1,2,3,4), B={3,4,5,6}, then
,b,c) : Given, A={1,2,3,4}B={3,4,5,6}Then, by options -Options a :-A−B={1,2,3,4}−{3,4,5,6}A−B={1,2}B−A={3,4,5,6}−{1,2,3,4}={5,6}Option b :-B−A={3,4,5,6}−{1,2,3,4}Options c :-[(A−B)−(B−A)]∩A=[{1,2}−{5,6}]∩{1,2,3,4}={1,2}∩{1,2,3,4}={1,2}Option d :-[(A−B)−(B−A)]∪A=[{1,2}−{5,6}]∪{1,2,3,4}={1,2,}∪{1,2,3,4}={1,2,3,4}.So, we see that option (a, b, c) are correct.
116745 If A={4n−3n−1:n∈N} and B={9(n−1) : n∈N}, then
C If A={4n−3n−1:n∈N}And, B={9(n−1):n∈N}For n=1,A=4−3−1=0B=9(1−1)=0Forn=2, A=16−6−1=9 B=9(2−1)=9Forn=3, A=43−3×3−1 A=64−10=54 B=9(3−1)=18Using roster method -A={0,9,54,243,……}B={0,9,18,27,36,45,54……}So, A⊂B but A≠B
116747 The number of subsets containing exactly 4 elements of the set {2,4,6,8,10,12,14,16,18 \} is equal to
A Number of digits =9{2,4,6,8,10,12,14,16,18}Number of ways to choose 4 elements in given set are=9C4=9!4!×5!=9×8×7×64×3×2=9×7×2=126
116748 If n(A∪B)=97, n(A∩B)=23 and n (A−B)=39, then n(B) is equal to
C Given, n(A∪B)=97n(A∩B)=23n(A−B)=39n(A−B)=n(A∪B)−n(B)39=97−n(B)58=n(B)