Question

If the relation $R:A\to B$, where $A=\{1,2,3\}$ and $B=\{1,3,5\}$ is defined by $R=\left\{\right(x,y):x<y,x\in A,y\in B\}$, then

• A. $R=\left\{\right(1,3),(1,5),(2,3),(2,5),(3,5\left)\right\}$
• B. $R=\left\{\right(1,1\left)\right(1,5),(2,3),(3,5\left)\right\}$
• C. $R^{-1}=\left\{\right(3,1),(5,1),(3,2),(5,3\left)\right\}$
• D. $R^{-1}=\left\{\right(1,1),(5,1),(3,2),(5,3\left)\right\}$

Answer 1

Answer: (A)

$R=\left\{\right(1,3),(1,5),(2,3),(2,5),(3,5\left)\right\}$

Given $A=\{1,2,3\}$ and $B=\{1,3,5\}$

$R=\left\{\right(x,y):x<y,x\in A,y\in B\}$

Taking $x$ from set $A$,

For $x=1$ from set $A$,

$y=3$ or $y=5$ from set $B$ to satisfy $x<y$

For $x=2$, $y=3$ or $y=5$

For $x=3$, $y=5$

Hence $R=\left\{\right(1,3),(1,5),(2,3),(2,5\left)\right(3,5\left)\right\}$