Question

If $R$ is the relation from set $A=\{1,3,4,5\}$ to $B=\{1,5\}$ defined as $R=\left\{\right(x,y)\in R:y>x\},$ then

• A. Domain of $R=\{1,3,4\}$
• B. Range of $R=\left\{5\right\}$
• C. $R^{-1}=\left\{\right(5,1),(5,3),(5,4\left)\right\}$
• D. $n(A\cap B)=1$

Answer 1

Answer: (A), (B), (C)

The correct options are
A Domain of $R=\{1,3,4\}$
B Range of $R=\left\{5\right\}$
C $R^{-1}=\left\{\right(5,1),(5,3),(5,4\left)\right\}$

$A=\{1,3,4,5\},B=\{1,5\}$
$R=\left\{\right(1,5),(3,5),(4,5\left)\right\}$
Domain $=\{1,3,4\}$
Range $=\left\{5\right\}$
$R^{-1}=\left\{\right(5,1),(5,3),(5,4\left)\right\}$
$(A\cap B)=\{1,5\}$
$\Rightarrow n(A\cap B)=2$