Question

If $A=\{5,7,9,11\},B=\{9,10\}$ and $aRb$ means $a<b$ where $a\in A,b\in B,$ then which of the following are true?

• A. Co-domain of $R$ is $\{9,10\}.$
• B. Range of $R=$Co-domain of $R$
• C. $R=\left\{\right(5,9),(5,10),(7,9),(7,10),(9,10\left)\right\}$
• D. Domain of $R$ is $\{5,7,9\}.$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

Co-domain of $R$ is $\{9,10\}.$

B

Range of $R=$Co-domain of $R$

C

$R=\left\{\right(5,9),(5,10),(7,9),(7,10),(9,10\left)\right\}$

D

Domain of $R$ is $\{5,7,9\}.$

Given that $R$ is a relation such that $aRb$ mean $a<b.$
$\Rightarrow R=\left\{\right(5,9),(5,10),(7,9),(7,10),(9,10\left)\right\}$

$\Rightarrow \text{Domain}=\{5,7,9\},$ the set of all first coordinates of the ordered pairs that belong to $R$

Also, co-domain $=\{9,10\},$ the second set in the relation $R$

Range $=\{9,10\},$ the set of second components of the ordered pairs which belong to $R$