Question

Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and
B = {3, 4, 5}. Find A', B', A n B', AUB,
and hence show that (A U B)'= A' intersection B'.


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Answer 1

ANSWER :–

• A' = {1, 4, 5, 6}

• B' = {1, 2, 6}

• A ⋂ B' = {2}

• A U B = {2, 3, 4, 5}

EXPLANATION :–

GIVEN :–

• Universal set (U) = {1, 2, 3, 4, 5, 6}

• A = {2, 3}

• B = {3, 4, 5}

TO FIND :–

⮕ A' , B' , A ⋂ B' , A U B

⮕ (A U B)' = A' ⋂ B' (To prove)

SOLUTION :–

⮕ Let's find –

• A' = U - A = {1, 2, 3, 4, 5, 6} - {2, 3} = {1, 4, 5, 6}

• B' = U - B = {1, 2, 3, 4, 5, 6} - {3, 4, 5} = {1, 2, 6}

• A ⋂ B' = {2, 3} ⋂ {1, 2, 6} = {2}

• A U B = {2, 3} U {3, 4, 5} = {2, 3, 4, 5}

⮕ Now Let's prove –

(A U B)' = A' ⋂ B'

L.H S. :–

= (A U B)'

= U - (A U B)

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

= {1, 6}

R.H.S. :–

= A' ⋂ B'

= {1, 4, 5, 6} ⋂ {1, 2, 6}

= {1, 6}

L.H.S. = R.H.S. (Hence proved)

EXTRA INFORMATION :–

• UNION OF TWO SETS :–

A set of element , which contains those elements which are in A, in B, or in both A and B is called Union.

• INTERSECTION OF TWO SETS :–

A set of element , which contains those elements which are present in both sets , is called INTERSECTION .