Question

Let A= {0, 1, 2, 3, 4, 5}, B= {2, 4, 6, 8} and C= {1, 3, 5, 7} .
Verify (A ∩ B) ∩ C = A ∩ (B ∩ C)

Answer 1

Solution :

(A ∩ B) ∩ C:

A ∩ B = {0, 1, 2, 3, 4, 5} ∩ {2, 4, 6, 8}

= {2,4}

(A∩B) ∩ C = {2,4} ∩ {1, 3, 5, 7}

= { }

A ∩ (B ∩ C)

B ∩ C = {2, 4, 6, 8} ∩ {1, 3, 5, 7}

= { }

A ∩ (B ∩ C) = {0, 1, 2, 3, 4, 5} ∩ { }

= { }

(A ∩ B) ∩ C = A ∩ (B ∩ C)

Hence it is verified.