Question

If $R$ is the relation 'less than' from, $A=\{1,2,3,4,5\}$ to $B=\{1,4,5\}$, then the set of ordered pairs corresponding to $R$ is

• A. $\{(1,4),(1,5),(2,5),(3,5),(4,5)\}$
• B. $\{(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)\}$
• C. $\{(5,2),(4,5),(5,3),(5,2),(5,1)\}$
• D. None of these

Answer 1

Answer: (B)

It is given that $\left(x,y\right)\in R\iff x<y$, where $x\in A$ and $y\in B$.
For the elements of the given sets $A$ and $B$, we find that
$1<4$, $1<5$, $2<4$, $2<5$, $3<4$, $3<5$ and $4<5$
$\therefore \left(1,4\right)\in R,\left(1,5\right)\in R,\left(2,4\right)\in R,\left(2,5\right)\in R,\left(3,4\right)\in R,\left(3,5\right)\in R$ and $\left(4,5\right)\in R$.
Thus, $R=\left\{\left(1,4\right),\left(1,5\right),\left(2,4\right),\left(2,5\right),\left(3,4\right)\left(3,5\right),\left(4,5\right)\right\}$.