Question

Let R be a relation in N defined by $(x,y)ϵR\iff x+2y=8$. Express R and $R^{-1}$ as sets of ordered pairs.

Answer 1

We have,

$(x,y)ϵR\iff x+2y=8$

Now,

$x+2y=8\Rightarrow x=8-2y$

Putting y = 1, 2, 3, we get x = 6, 4, 2 respectively

For y = 4, we get $x=0\text{/}ϵN$

Also, for $y>4,x\text{/}ϵN$

$\therefore R=$ {(6, 1), (4, 2), (2, 3)}

Thus,

$R^{-1}=\left\{\right(1,6),(2,4),(3,2\left)\right\}$

$\Rightarrow R^{-1}=\left\{\right(3,2),(2,4),(1,6\left)\right\}$