Question

If the relation $R:A\to B$ where $A=\{1,2,3\}B=\{1,3,5\}$ 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. $R=\left\{\right(1,1),(1,5),(2,3),(3,5\left)\right\}$
• 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

The correct option is A $R=\left\{\right(1,3),(1,5),(2,3),(2,5),(3,5\left)\right\}$

$(x,y)$ satisfying $x<y$

$\left\{1\right\}$ can be mapped or related to $\{3,5\}$

$\left\{2\right\}$ can be mapped or related to $\{3,5\}$

$\left\{3\right\}$ can be mapped or related to $\left\{5\right\}$

$\therefore$ Relation R is $\{(1,3),(1,5)(2,3),(2,5)(3,5)\}$