Question:
Mark (√) against the correct answer in the following:
Let A and B be two non - empty sets and let
$f:(A \times B) \rightarrow(B \times A): f(a, b)=(b, a) .$ Then, $f$ is
A. one - one and into
B. one - one and onto
C. many - one and into
D. many - one and onto
Solution:
SINCE, f(a, b) = (b, a).There is no same value of y at different values of x∴function is one one
$\therefore$ Range $(A \times B) \neq$ Codomain $(B \times A)$
$\Rightarrow$ function is into