Question

Find, which of the following sets are singleton sets:
$B=\{y:2y+1<3andy\in W\}$

Answer 1

Given: $B=\{y:2y+1<3andy\in W\}$

We know that singleton set is a set containing only one element and it is also called a unit set.

As, 2y + 1 < 3, $y\in W$
$\Rightarrow$ 2y < 3 - 1, $y\in W$
$\Rightarrow$ 2y < 2, $y\in W$
$\Rightarrow$ $y<\frac{2}{2}$, $y\in W$
$\Rightarrow$ y < 1 and $y\in W$
$\Rightarrow$ y = 0
$\Rightarrow$ B = {0}

So, B has only one element in it.

Hence, the set $B=\{y:2y+1<3andy\in W\}$ is a singleton set.