Truth Set

The set of all values $x$ that makes statement $P(x)$ true.

Example

Find truth set of $P(x)$ where $P(x)$ is $x^2-4x+3=0$. So, we find all values of x that makes this true. In this case, the truth set is $\{1,3\}$

Empty Truth Set Example

Find the truth set for $P(x)$ where $P(x)$ is $x^2+3=0$. The truth set is $\varnothing$. There are no values of x for this.

Set Builder Notation Example