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Let A and B be two sets. Show that f: Ax...

Let `A` and `B` be two sets. Show that `f: AxxB->BxxA` defined by `f(a ,\ b)=(b ,\ a)` is a bijection.

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`f:AxxB→BxxA` is defined as `f(a,b)=(b,a)`
Let `(a_1,b_1),
(a_2,b_2)inAxxB`
such that
`f(a_1,b_1)=f(a_2,b_2).`
`=>(b_1,a_1)=(b_2,a_2)`
`=>(b_1=b_2)` and `(a_1=a_2)`
`=>(a_1,b_1)=(a_2,b_2)`
`thereforef` is one-one. ...
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