Question

If $R$ is a relation from $A$ to $B$ defined by $R=\left\{\right(x,y)|x<y,x\in A,y\in B\}$ where $A=\{1,2,3,4,5,6,7\}$ and $B=\{1,4,5\}$, then $R^{-1}$ equals

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

Answer 1

The correct option is C $\left\{\right(4,1),(5,1),(4,2),(5,2),(4,3),(5,3),(5,4\left)\right\}$

It is given that $(x,y)\in R\iff x<y$ such that $x\in A,y\in B$
$\therefore R=\left\{\right(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5\left)\right\}$
$\therefore R^{-1}=\left\{\right(4,1),(5,1),(4,2),(5,2),(4,3),(5,3),(5,4\left)\right\}$