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Show that {A}{B}={A}{C}need not imply {B}={C}.

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Show that $A \cap B = A \cap C$ need not imply $B = C$ .

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Harper Discussed

Show that

A \cap B = A \cap C

need not imply

B = C

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Solution: We can show this by taking some example sets.
Let,

A = {1, 2, 3}

B = {2, 3, 4}

C = {2, 3, 5}

Then,

A \cap B = {2, 3}

and

A \cap C = {2, 3}

Thus,

A \cap B = A \cap C

even if B is not equal to C.

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Question Text	Show that $A \cap B = A \cap C$ need not imply $B = C$ .
Answer Type	Text solution:1
Upvotes	150