Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the identities A ∩ (B – C) = (A ∩ B) – (A ∩ C)

Asked by Aaryan | 1 year ago |  60

1 Answer

Solution :-

A ∩ (B – C) = (A ∩ B) – (A ∩ C)

B–C is defined as {x  B: x ∉ C}

B = {2, 3, 5, 6}

C = {4, 5, 6, 7}

B–C = {2, 3}

Firstly let us consider the LHS

(A ∩ (B – C)) = {x: x  A and x  (B – C)}

= {2}

Now, RHS

(A ∩ B) = {x: x  A and x  B}

= {2, 5}

(A ∩ C) = {x: x  A and x  C}

= {4, 5}

(A ∩ B) – (A ∩ C) is defined as {x  (A ∩ B): x ∉ (A ∩ C)}

= {2}

LHS = RHS

Hence Verified.

Answered by Sakshi | 1 year ago

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