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If A,B and C are three sets such that A ...

If A,B and C are three sets such that `A cap B = A cap C and A cup B = A cup C ` then

A

A=B

B

A=C

C

B=C

D

`A cap B = phi `

Text Solution

Verified by Experts

The correct Answer is:
C
`B=B cap (A cup B)`
`=B cap (A cup C)" " (therefore A cup B= A cup C)`
`=(B cap A)cup (B cap C ) `
`= (B cap A)cup (B cap C) `
`= ( A cap B )cup (B cap C) `
`(A cap C) cup (B cap C) " " (therefore A cap B = A cap C)`
`=(A cup C) cap C`
`(A cup C)cap C`
=C
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