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Mark (√) against the correct answer in the following:

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

 

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