Question

If A={1,2,3,4,5}, A∩B={3,4,5} and A∪B={1,2,3,4,5,6}, find the set B.

Answer 1

Answer:

U = {1,2,3,4,5,6}

A = {2,3}

B = {3,4,5}

A∪B={2,3} ∪ {3,4,5} = {2,3,4,5}

Therefore, (A∪B)

= {1,6}

Also, A

= {1,4,5,6}

B

= {1,2,6}

Therefore, A

∩B

= {1,4,5,6} ∩ {1,2,6} = {1,6}

Hence, (A∪B)

=A

∩B