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

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Solution

If A is the set of natural numbers; and
B is the set of all even natural numbers; and
C is the set of all even integers, then
A intersection B = Set of all even numbers = A intersection C
But here B and C are not equal.

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Similar questions

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

A \cap B = A \cap C

B = C

For three sets A, B and C, show that

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

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

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