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

Answer:

L.H.S = A ∪ (B ∪ C)

= {1,2,3,4,5} ∪ [{2,3,5,6} ∩ {4,5,6,7}]

= {1,2,4,5} ∪ {5,6}

= {1,2,4,5,6} R.H.S = (A ∪ B) ∩ (A ∪ C)

= [{1,2,4,5} ∪ {2,3,5,6}] ∩ [{1,2,4,5} ∪ {4,5,6,7}] = {1,2,3,4,5,6} ∩ {1,2,4,5,6,7}

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

∴ L.H.S = R.H.S

Answer 2

Answer:

(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.