Question

Given A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8, 10} and C = {1, 3, 5, 6, 9}.

Prove that A ∩ (B − C) = (A ∩ B) − (A ∩ C).​

Answer 1

Answer:

B - C = {2,4,8,10}

A ∩ (B − C)={1,2,3,4,5,6} ∩ {2,4,8,10}

= {2,4}

Now, (A ∩ B) = {2,4,6}

(A ∩ C)= {1,3,5,6}

(A ∩ B) − (A ∩ C) = {2,4,6} - {1,3,5,6}

= {2,4}

Therefore,

A ∩ (B − C) = (A ∩ B) − (A ∩ C).

Step-by-step explanation:

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