If A and B are two sets, then prove that :
`A cupB=A capBhArrA=B`.

Explanation

Let `A = B`
`:. A cupB=A cupA=A`
and `A capB=A capA=A`
`rArr A cupB=A cap B`
Again, let `A cup B=AcapB`
To prove `A =B`
Let `x in A`
`rArr xin A cap B`
`rArrx in A capB(becauseA cup B=A capB)`
`rArrx in A and x in B`
`rArr x in B`
`:. A sube B` ....(1)
Let `x in B`
`rArr x in A cup B`
`rArr x in A cap B(because A cup B=A cap B)`
`rArr x in A and x in B`
`rArr x in A`
`:. B sube A` ....(2)
From eqs. (1) and (2)
`A = B`
Therefore,
`A cupB=AcapB hArrA=B`. Hence Proved.