Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Then, f is:

Question

Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let $f$ = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Then, $f$ is:

Smart Achievers · Accepted Answer

(1)

Ans. one-one but not onto

Explanation:

Here, $f : A \to B$ is defined as {(1, 4),(2, 5),(3, 6)}.

Since, the image of distinct elements of A under $f$ are distinct as:

$f (1) = 4,$ $f (2) = 5$ and $f (3) = 6$

From above it is evident that

$x_{1} \neq x_{2}$ and $f (x_{1}) \neq f (x_{2})$

$∴$ $f : A \to B is one-one.$

Here, Co-domain of $f \neq$ Range of $f$

Hence, $f$ is not onto.

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