The given sets are U={4,8,12,16,20,24,28}, A={8,16,24} and B={4,16,20,28}
We know that the complement of set A is A′=U−A.
Consider the following:
(A∪B)′=U−(A∪B)={4,8,12,16,20,24,28}−[{8,16,24}∪{4,16,20,28}]
={4,8,12,16,20,24,28}−{4,8,16,20,24,28}={12}......(1)
A′∩B′=[U−A]∩[U−B]=[{4,8,12,16,20,24,28}−{8,16,24}]∩[{4,8,12,16,20,24,28}−{4,16,20,28}]
={4,12,20,28}∩{8,12,24}={12}......(2)
From equations 1 and 2, we get that (A∪B)′=A′∩B′.
Hence, (A∪B)′=A′∩B′.