Question

Let for two sets $A$ and $B,$ $A\times B=\left\{\right(1,3),(2,3),(3,4),(2,5),(5,7),(1,6\left)\right\}$, and a relation $R$ is defined from $A$ to $B,$ then the correct options is/are

• A. $R^{-1}=\left\{\right(x,y):x,y\in N,x>y,x+y=7$
• B. Domain of $R$ can be $\{1,2,3,5\}$
• C. Range of $R$ can be $\{3,5,7\}$
• D. Co domain of $R$ is $\{3,4,5,6,7\}$

Answer 1

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

The correct options are
A $R^{-1}=\left\{\right(x,y):x,y\in N,x>y,x+y=7$
B Domain of $R$ can be $\{1,2,3,5\}$
C Range of $R$ can be $\{3,5,7\}$
D Co domain of $R$ is $\{3,4,5,6,7\}$

If $x,y\in N,x>y,x+y=7$
$x=6,y=1\Rightarrow (x,y)=(6,1)$
$x=5,y=2\Rightarrow (x,y)=(5,2)$
$x=4,y=3\Rightarrow (x,y)=(4,3)$
Here, $B\times A=\left\{\right(3,1),(3,2),(4,3),(5,2),(7,5),(6,1\left)\right\}$
and $R^{-1}\subset B\times A$

Domain can be the first element of ordered pair from $A\times B$
$\therefore$ Domain of $R$ can be $\{1,2,3,5\}$

Range can be the second element of ordered pair from $A\times B$
$\therefore$ Range of $R$ can be $\{3,5,7\}$

Co domain is set of all the second elements of ordered pair from $A\times B$
$\therefore$ Co domain of $R$ is $\{3,4,5,6,7\}$