Question

$\{1,2,3,4\}$ is the domain of which of the relation $R$ given in the following options?

• A. $R=\left\{\right(2,1),(3,4),(5,6),(7,8\left)\right\}$
• B. $R=\left\{\right(1,1),(2,2),(3,3),(4,4\left)\right\}$
• C. $R=\left\{\right(3,1),(5,2),(7,3),(9,4\left)\right\}$
• D. $R=\left\{\right(1,1),(1,2),(1,3),(1,4\left)\right\}$

Answer 1

The correct option is B $R=\left\{\right(1,1),(2,2),(3,3),(4,4\left)\right\}$

$\underset{–}{ConceptInvolved:}$

Domain is the collection of the first elements of all the ordered pairs in a relation.

$\underset{–}{Method:}$

Domain of the relation $R=\left\{\right(2,1),(3,4),(5,6),(7,8\left)\right\}$ is $\{2,3,5,7\}$.

Domain of the relation $R=\left\{\right(1,1),(2,2),(3,3),(4,4\left)\right\}$ is $\{1,2,3,4$}.

Domain of the relation $R=\left\{\right(3,1),(5,2),(7,3),(9,4\left)\right\}$ is $\{3,5,7,9\}$.

Domain of the relation $R=\left\{\right(1,1),(1,2),(1,3),(1,4\left)\right\}$ is $\left\{1\right\}$.

So, only option 'b' has the relation $R$ which has domain as $\{1,2,3,4\}$.