Question

Let N be the set of all natural numbers. Let $R=\left\{\right(a,b):a,bϵN\text{and}2a+b=10\}$. Show that R is a binary relation on N. Find its domain, range and co-domain.

Answer 1

Here $R=\left\{\right(a,b):a,bϵN\text{and}2a+b=10\}$

Now, $2a+b=10\Rightarrow b=(10-2a)$

$\therefore (a=1\Rightarrow b=8),(a=2\Rightarrow b=6),(a=3\Rightarrow b=4),(a=4\Rightarrow b=2)$

$\therefore R=\left\{\right(1,8),(2,6),(3,4),(4,2\left)\right\}$

Since $R\subset N\times N$, so R is a binary relation on N.

Dom (R) = set of 1st coordinates of elements of R.

= {1, 2, 3, 4}

Range (R) = set of 2nd coordinates of elements of R.

= {8, 6, 4, 2}

Co-domain of R = N.