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# Let A and B be sets. Show that f : A × B → B × A such that f (a, b) = (b, a) is bijective function.

Q. 8 Let A and B be sets. Show that $f : A \times B \rightarrow B \times A$ such that $f (a, b) = (b, a)$ is
bijective function.

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$f : A \times B \rightarrow B \times A$

$f (a, b) = (b, a)$

Let $(a_1,b_1),(a_2,b_2) \in A\times B$

such that  $f (a_1, b_1) = f(a_2, b_2)$

$(b_1,a_1)=(b_2,a_2)$

$\Rightarrow$     $b_1= b_2$   and   $a_1= a_2$

$\Rightarrow$          $(a_1,b_1) = (a_2,b_2)$

$\therefore$    f is one- one

Let,  $(b,a) \in B\times A$

then there exists $(a,b) \in A\times B$  such that  $f (a, b) = (b, a)$

$\therefore$ f is onto.

Hence, it is bijective.

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