We have,
U={1,2,3,4,5,6,7,8,9}
A={2,4,6,8}
B={2,3,5,7}
Since,
(A∩B)′=U−(A∩B)
(A∩B)′={1,2,3,4,5,6,7,8,9}−({2,4,6,8}∩{2,3,5,7})
(A∩B)′={1,2,3,4,5,6,7,8,9}−{2}
(A∩B)′={1,3,4,5,6,7,8,9}
Now,
A′∪B′=(U−A)∪(U−B)
A′∪B′=({1,3,5,7,9}−{2,4,6,8})∪({1,4,6,8,9}−{2,3,5,7})
A′∪B′={1,3,5,7,9}∪{1,4,6,8,9}
A′∪B′={1,3,4,5,6,7,8,9}
It is clear that,
(A∩B)′=A′∪B′
Hence, proved.