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Universe set and truth set of an equation


Consider the set THE = {0, 1, 2, 3, 4, 5} and the equation x + 2 = 5.

Note that set number 3 THE is called universe set of the equation and the set {3} is the truth set of this same equation.

Note this other example:

  • Determine the integers that satisfy the equation x² = 25.

The set of integers is the universe set of the equation. The numbers -5 and 5, which satisfy the equation, form the truth set and can be indicated by:
V = {-5.5}.

Hence, we conclude that:

Universe set is the set of all values ​​the variable can assume. It is indicated by U. Truth set is the set of values ​​of U that make the equation true. It is indicated by V.

Comments:

  • The truth set is a subset of the universe set.

  • Not being mentioned the universe set, we must consider as a universe set the set of rational numbers.

  • The truth set is also known as solution set and may be indicated by s.
Next: Roots of an Equation