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Question

Show that AB=AC need not imply B=C.

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Solution

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

AB = {1, 2, 3, 4} {2, 3, 4, 5, 6}

= {2, 3, 4}

AC = {1, 2, 3, 4} {2, 3, 4, 9, 10}

= {2, 3, 4}

Now we have

AB=AC

But BC.


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