If A={1,3,5,7,9,11,13,15,17}, B={2,4,...18}and N={1,2,3,4......18} is the universal set then A'∪((A∪B)∩B') is
A
B
A∪B
N
Explanation for correct option:
Step1. Given,
A={1,3,5,7,9,11,13,15,17},
B={2,4,...18}
N={1,2,3,4,5,6.......16,17,18}
A'=N-A={2,4,6,...18}=BB'=N-B={1,3,5,...17}=AN=A∪B={1,2,3,4,....17,18}N∩B'={1,3,5,...17}=A
Since, N is universal set then A∪B=N
Step2. Finding value for Á∪((A∪B)∩B́):
Now,
Á∪((A∪B)∩B́)=Á∪(N∩B́){A∪B=N}=A'∪A{N∩B'=A}=B∪A{A'=B}=N
Hence, The correct option is (D).
If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B ={2, 4, ......, 18} and N, the set of natural numbers is the universal set, then (A′∪[(A∪B)∩B′]) is