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=B

A=C

B=C

`A cap B = phi `

Text Solution

Verified by Experts

The correct Answer is:

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

A=B

B=C

A`subset`B

B`subset`A

If A and B are two sets then A cup B=A cap B if and only if

A`sube`B

B`sube`A

A=B

A`!=`B

If A and B are two given sets then A cap (A capB)^(c) is equal to

`phi`

A`capB^(c)`