Question

Q3. Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}. Find A′, B′ , A′ ∩ B′, A ∪ B and hence show
that ( A ∪ B )′ = A′ ∩ B′.

please write in a short way, please

Answer 1

Explanation :

U = {1,2,3,4,5,6} , A={2,3} and B={3,4,5}

therefore ,

A'= {1,4,5,6}

B'={1,2,6}

A′ ∩ B′ = {1,6}

Now to show ( A ∪ B )′ = A′∩ B′ , first find ( A ∪ B )

(A U B) = {2,3,4,5,}

Now, ( A ∪ B )′ = {1,6}

As we have already know, A′ ∩ B′ = {1,6}

therefore, ( A ∪ B )′ = A′∩ B′

Additional information :

1] what is complement of set? :

consider A is the set, which is subset of the universal set U. then