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Question

Let A, B and C be the sets such that AB=AC and AB=AC. Show that B=C.

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Solution

We know that A=A(AB) and A=A(AB)

Now AB=AC and AB=AC

B=B(BA)=B(AB)

=B(AC) [ AB=AC]

=(BA)(BC) (By distributive law)

=(AB)(BC)

=(AC)(BC) [ AB=AC]

=(CA)(CB)

=C(AB) (By distributive law)

=C(AC) [ AB=AC]

=C(CA)=C Hence B=C


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