Identify the empty set $,$ the singleton set and the pair set $.$
$D = {x : 5 x - 4 = 0, x \in W}$

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Solution

The given set-builder form is $D = {x : 5 x - 4 = 0, x \in W}$
In the set $D$ $,$ $5 x - 4 = 0$ and $x \in W$
$5 x - 4 = 0$
$5 x = 4$
$x = \frac{4}{5}$
$\frac{4}{5} \notin W$
The given set has no element $.$
The roster form of the given set-builder form is given below
$D = \{\}$
$n (D) = 0$ $,$ the set $D$ is a empty set
Hence $,$ the given set $D = {x : 5 x - 4 = 0, x \in W}$ is an empty set

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