If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that:

Question

Philoid · Accepted Answer

(A ∩ B}’ = A’ ∪ B.’

(A ∩ B) = {x:x ϵ A and x ϵ B }.

= {7}

(A∩B)’ means Complement of (A∩B) with respect to universal set U.

So, (A∩B)’ = U–(A∩B)

U–(A∩B)’ is defined as {x ϵ U : x ∉ (A∩B)’}

U = {2, 3, 5, 7, 9}

(A∩B)’ = {7}

U–(A∩B)’ = {2, 3, 5, 9}

A’ means Complement of A with respect to universal set U.

So, A’ = U–A

U–A is defined as {x ϵ U : x ∉ A}

U = {2, 3, 5, 7, 9}

A = {3, 7}

A’ = {2, 5, 9}

B’ means Complement of B with respect to universal set U.

So, B’ = U–B

U–B is defined as {x ϵ U : x ∉ B}

U = {2, 3, 5, 7, 9}

B = {2, 5, 7, 9}.

B’ = {3}

A’ ∪ B’ = {x: x ϵ A or x ϵ B }

= {2, 3, 5, 9}

Hence verified.