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Question

If A = {a,b}, B = {b,c} and C = {b,c,d} ; then A × (B C) = _____ .

A
(A B) × C
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B
(A B) × C
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C
(A B) C
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D
(A × B) (A × C)
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Solution

The correct option is D (A × B) (A × C)
Let us write the set of (B C) first.
(B C) = {b,c,d}
A × (B C) = {(a,b),(a,c),(a,d),(b,b),(b,c),(b,d)}
Now Let us verify the given options :

(a) A B = {a,b,c}
(A B) × C = {(a,b),(a,c),(a,d),(b,b),(b,c),(b,d),(c,b),(c,c),(c,d)}

(b) A B = {b}
(A B) × C = {(b,b),(b,c),(b,d)}

(c) A B = {a,b,c}
(A B) C = {a,b,c,d}

(d) (A × B) = {(a,b),(a,c),(b,b),(b,c)}
(A × C) = {(a,b),(a,c),(a,d),(b,b),(b,c),(b,d)}
(A × B) (A × C) = {(a,b),(a,c),(a,d),(b,b),(b,c),(b,d)} which is equal to
A × (B C)

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