Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3,

1.	Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that: (A ∩ B}’ = A’ ∪ B’.
Answer» (A ∩ B) = {x:x ϵ A and x ϵ B}. = {2} (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 = {1, 2, 3, 4, 5, 6, 7, 8, 9} (A∩B)’ = {2} U – (A∩B)’ = {1, 3, 4, 5, 6, 7, 8, 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 = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {2, 4, 6, 8} A’ = {1, 3, 5, 7, 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 = {1, 2, 3, 4, 5, 6, 7, 8, 9} B = {2, 3, 5, 7}. B’ = {1, 4, 6, 8, 9} A’ ∪ B’ = {x: x ϵ A or x ϵ B} = {1, 3, 4, 5, 6, 7, 8, 9} Hence verified

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that: (A ∩ B}’ = A’ ∪ B’.

Answer»

(A ∩ B) = {x:x ϵ A and x ϵ B}.

= {2}

(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 = {1, 2, 3, 4, 5, 6, 7, 8, 9}

(A∩B)’ = {2}

U – (A∩B)’ = {1, 3, 4, 5, 6, 7, 8, 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 = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {2, 4, 6, 8}

A’ = {1, 3, 5, 7, 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 = {1, 2, 3, 4, 5, 6, 7, 8, 9}

B = {2, 3, 5, 7}.

B’ = {1, 4, 6, 8, 9}

A’ ∪ B’ = {x: x ϵ A or x ϵ B}

= {1, 3, 4, 5, 6, 7, 8, 9}

Hence verified