Question

If R be a relation < from $A=1,2,3,4toB=1,3,5$, i.e.(a, b) $\in$ R if $a<b$, then $Ro{R}^{-1}$ is

• A. $(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)$
• B. $(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)$
• C. $(3,3),(3,5),(5,3),(5,5)$
• D. $(3,3),(3,4),(4,5)$

Answer 1

Answer: (C)

$(3,3),(3,5),(5,3),(5,5)$

R: A$\in B$ under given condition $a<b$ is given by

$R=(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)$

$R^{-1}=(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)$

$Ro{R}^{-1}=3,1),(5,1),(3,2),(5,2),(5,3),(5,4)$

$Ro{R}^{-1}$: For composing $Ro{R}^{-1}$ we will pick up an element of $R^{-1}$ first and then of R

(3, 1) $\in R^{-1}(1,3)\in R\to (3,3)\in Ro{R}^{-1}$

$\therefore Ro{R}^{-1}=(3,3),(3,5),(5,3),(5,5)$ only.

Elements are not repeated on a set.