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If the sets A,B are such that A cup B=B ...

If the sets A,B are such that `A cup B=B cap A` thrn show that A=B

Text Solution

Verified by Experts

We have `A cap B = A cup B `
Consider the following cases:
(i)` A sub B = A and cup B = Bm So, `
`A cap B ne A cup B `
(ii) `B sub A`
For this case ,` A cap B = B and A cup B` = A, So ,
`A cap B ne A cap B `
(iii) A and B are disjoint
For this case `A cap B = phi " and " A cup B `= set of all element of set A and set B
`So, A cap B ne A cup B `
(iv) Sets A and B have some elements common
for this case , `A cap B` have some elements but ` A cap B ` is the
So ,` A cap B ne A cup B `
From the above cases ,we conclude that sets A and B are same . So A= B .
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