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.

Answers (1)

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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