Relations and Functions

Relations and Functions

Question

Show that A ∩ B = A ∩ C need not imply B = C.

Answer

Let       A = {a, b, c, d}, B = {b, c, d, e, f},  C  = {b, c ,d, l, m}
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From (i) and (ii), we have
      space space space space space space space space space space straight A intersection straight B space equals space straight A intersection straight C
But,      space space space space space space space straight B space not equal to space straight C

Hence,   space space space space straight A intersection straight B space equals space straight A intersection straight C space need not imply B = C

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