Question

If $A=\{1,2,3\},B=\{1,4,6,9\}$ and $R$ is a relation from $A$ to $B$ defined by '$a$ is greater than $b$' where $a\in A,b\in B$.
Then the range of $R$ is

• A. None of these
• B. $\left\{1\right\}$
• C. $\{1,4,6,9\}$
• D. $\{4,6,9\}$

Answer 1

The correct option is B $\left\{1\right\}$

Given: $R$ is a relation from $A=\{1,2,3\}\text{to}B=\{1,4,6,9\}$ defined by '$a$ is greater than $b$'.

For a relation $R$ we have
Domain of $R=\left\{a|\right(a,b)\in R\}$ and
Range of $R=\left\{b|\right(a,b)\in R\}$

Here, $R=\left\{\right(a,b)|a>b,a\in A,b\in B\}$
$R=\left\{\right(2,1),(3,1\left)\right\}$

Hence, range of $R=\left\{1\right\}$