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  4. The function f: A →B is given by f (x) = x, x ϵ A, is one to one but not onto. Then

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Q. The function $f$ : A →B is given by $f (x) = x, x \epsilon A$, is one to one but not onto. Then

KEAMKEAM 2016Relations and Functions - Part 2

Solution:

$f(x)=x$ is identity function.
It is given that $f(x)$ is one to one but not on to.
It means some element in $B$ has no pre image in $A$.
$\Rightarrow A \subset B$