A truth set is the set of all possible inputs in it's domain for which a predicate is true. Formally the truth set is defined as follows

If is a predicate and has domain , the truth set of is the set of all elements of that make true when they are substituted for . The truth set of is denoted in set builder notation.

Example

Let be the predicate " is a factor of 8." Find the truth set of if

a. The Domain of is the Set of All Positive Integers

The truth set of is because those are the only positive integers that evenly divide 8.

b. The Domain of is the Set of All Integers

The truth set of is because additionally the negative integers also evenly divide 8.