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Question

If A={a,b},B={x,y} and C={a,c,y}, then verify that A×(BC)=(A×B)(A×C)

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Solution

BC={x,y}{a,c,y}={y}

A×(BC)={a,b}×{y}

={(a,y),(b,y)}

A×(BC)={(a,y),(b,y)} ..........(1)

A×B={a,b}×{x,y}={(a,x),(a,y),(b,x),(b,y)}

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

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

={(a,y),(b,y)} .........(2)

From (1) and (2) we have

A×(BC)=(A×B)(A×C)

Hence verified.

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