show that A∩ B=A∩ C need not imply B=C

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A \cap B = A \cap C

B = C

Show that A intersection B is equal to A intersection C need not imply B=C

For three sets A, B and C, show that

(i) $A \cap B = A \cap C$ need not imply B = C.

(ii) $A \subset B \Rightarrow C - B \subset C - A$

\to a \times \to b = \to a \times \to c

\to b = \to c

A \cup B = A \cap B

A = B

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