Question

Let $A=\left\{a,b,c\right\}$ and $B=\left\{1,2\right\}$. Consider a relation $R$defined from set $A$ to set $B$.Then $R$is equal to set

• A. $A$
• B. $B$
• C. $A\times B$
• D. $B\times A$

Answer 1

The correct option is C

$A\times B$

Explanation for the correct answer:

Given,

A relation $R$defined from set $A$ to set $B$ is a set of ordered pairs $(a,b)$ such that $a\in A$ and $b\in B$.

$A=\left\{a,b,c\right\}$ and $B=\left\{1,2\right\}$

$\Rightarrow A\times B=\left\{\left(a,1\right),\left(a,2\right),\left(b,1\right),\left(b,2\right),\left(c,1\right),\left(c,2\right)\right\}$

Now relation $R$ will be a subset of $A\times B$

Therefore, $R=A\times B$ is a possible set.

Hence, option (C) is the correct answer.