Question

If $A=\{a,b,c,d\}$,& $B=\{1,2,3\}$, which of the following sets of ordered pairs are not relations from $\mathit{A}\mathbf{}\mathit{t}\mathit{o}\mathbf{}\mathit{B}$?

• A. $\left\{\right(a,1),(a,3\left)\right\}$
• B. $\left\{\right(b,1),(c,2),(d,1\left)\right\}$
• C. $\left\{\right(a,2),(b,3),(3,b\left)\right\}$
• D. $\left\{\right(a,1),(b,2),(c,3\left)\right\}$

Answer 1

The correct option is C

$\left\{\right(a,2),(b,3),(3,b\left)\right\}$

Explanation for correct option.

Given, $A=\{a,b,c,d\}$, & $B=\{1,2,3\}$,

A relation from $AtoB$is define as $(x,y),suchthatx\in A\&y\in B$

$\left\{\right(a,2),(b,3),(3,b\left)\right\}$

In the above set

$$\begin{gathered} (a,2)\&(b,3)\in A\times B \\ But(3,b)\notin A\times B \end{gathered}$$

Hence, the correct option is $\mathbf{\left(}\mathit{C}\mathbf{\right)}$.