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Let A and B be sets. If A nnX = B nnX =v...

Let A and B be sets. If `A nnX = B nnX =varphi`and `A uuX = B uuX`for some set X, show that `A = B`.(Hints `A = A nn(A uuX), B = B nn(B uuX)`and use Distributive law)

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`A= A nn (A uu X)`
`= A nn (B uu X)`
`= (A nn B) uu (A nn X)`
`=(A nn B) uu phi` (by distributive law)
`A = Ann B` eqn(1)
now `B= B nn (B uu X)`
`= B nn (A uu X)`
`= (B nn A) uu (B nn X)`
...
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