Question

If f(A) is a proper subset of B, then $f:A\to B$ is called a/an ......... function.

• A. into
• B. onto
• C. one - one
• D. indentity

Answer 1

The correct option is A into

$\Rightarrow$ A function is said to be an into function from Set $A$ to set $B,$ if at-least one element of B is not connected to an element of $A.$

$\Rightarrow$ Here, when $A$ is a proper subset of $B,$ clearly, it will have lesser elements than set $B,$ and those extra elements of set $B$ will not be connected to any element of Set $A.$ So it is an into function.

$\therefore$ If $f\left(A\right)$ is a proper subset of $B,$ then $f:A\to B$ is called an $into$ function.