Question

If $A=\{1,2,3\}andB=\{2,3,4\}$, then which of the following relations is a function from $\mathrm{A}$ to $B$?

• A. $\left\{\right(1,2),(2,3),(3,4),(2,2\left)\right\}$
• B. $\left\{\right(1,2),(2,3),(1,3\left)\right\}$
• C. $\left\{\right(1,3),(2,3),(3,3\left)\right\}$
• D. $\left\{\right(1,1),(2,3),(3,4\left)\right\}$

Answer 1

The correct option is C

$\left\{\right(1,3),(2,3),(3,3\left)\right\}$

Explanation for the correct option:

Function:This means that if the object $x$ is in the set of inputs (called the domain) then a function $f$ will map the object $x$ to exactly one object$f(x)$ in the set of possible outputs (called the codomain).

Given,$A=\{1,2,3\}$ & $\mathrm{B}=\{2,3,4\}$

Option C:$\left\{\right(1,3),(2,3),(3,3\left)\right\}$

Domain is mappen uniquely with co-domain.

Hence, correct option is option(C).

Explanation for the in-correct option:

Option A: $\left\{\right(1,2),(2,3),(3,4),(2,2\left)\right\}$

With respect to $x=2$we have two images.

Option B $\left\{\right(1,2),(2,3),(1,3\left)\right\}$

With respect to $x=1$we have two images.

Option D $\left\{\right(1,1),(2,3),(3,4\left)\right\}$

In codmain we don't have element $1$

Therefore mapping is not possible.

Hence, correct option is option(C) .