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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.

Text Solution

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`f:A×B→B×A `is defined as
`f(a,b)=(b,a).`
Let `(a_1,b_1),(a_2 ,b_2)∈A×B `
such that `f(a_1,b_1)=f(a_2,b_2).`
`⇒(b_1,a_1)=(b_2,a_2)` ...
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