Question

The function $f:A\to B$ given by $f\left(x\right)=x,x\in A$, is one to one but not onto. Then;

• A. $B\subset A$
• B. $A=B$
• C. $A^{\prime }\subset B^{\prime }$
• D. $A\subset B$
• E. $A^{\prime }\cap B^{\prime }=\varphi$

Answer 1

The correct option is D $A\subset B$

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