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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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Show that

A \cap B = A \cap C

need not imply

B = C

13 mins ago

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13 mins ago

Text solutionVerified

Let

A = {0, 1}

B = {0, 2, 3}

C = {0, 4, 5}

So,

A \cap B = {0}

and

A \cap C = {0}

Here,

A \cap B = A \cap C = {0}

However,

B \neq = C

2 \in B

and

2 \in / 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