InterviewSolution
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InterviewSolution
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Let A and B be sets. Show that `f" ":" "AxxB`,`BxxA`such that `f" "(a ," "b)" "=" "(b ," "a)`is bijective function. |
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Answer» In `f: AxxB to BxxA` `f(a, b) = (b, a) AA (a, b) in A xx B` Let `" " (a, b), (c, d) in AxxB` and `" " f(a, b) = f(c,d)` `rArr (b, a) = (d, c)` `rArr b =d and a = c ` `rArr (a, b) = (c, d)` `therefore f ` is one-one. Again, for each `(a, b) in B xx A, (b, a) in A xx B` is such that `therefore " " f(b, a) = (a, b)` `therefore f` is onto. Therefore, `f` is one-one onto function. |
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