The elements of the truth set of an equation are called **roots of the equation**. To check if a number is root of an equation, we must follow the following sequence:

Replace the unknown with this number.

Determine the value of each member of the equation.

Check for equality. Being a true sentence, the number considered is the root of the equation.

Examples:

Check which of the elements of the universe set are roots of the equations below, determining in each case the truth set.

Solve the equation

**x****- 2 = 0**, being*U*= {0, 1, 2, 3}.

For *x* = 0, we have: 0 - 2 = 0 => -2 = 0. (F)

For *x* = 1, we have: 1 - 2 = 0 => -1 = 0. (F)

For *x* = 2, we have: 2 - 2 = 0 => 0 = 0. **(V)**

For *x* = 3, we have: 3 - 2 = 0 => 1 = 0. (F)

We find that 2 is root of the equation *x -* 2 = 0, so *V* = {2}.

Solve the equation

**2**, being*x*- 5 = 1*U*= {-1, 0, 1, 2}.

For *x* = -1, we have: 2. (-1) - 5 = 1 => -7 = 1. (F)

For *x* = 0, we have: 2. 0 - 5 = 1 => -5 = 1. (F)

For *x* = 1, we have: 2. 1 - 5 = 1 => -3 = 1. (F)

For *x* = 2, we have: 2. 2 - 5 = 1 => -1 = 1. (F)

Equation 2*x* - 5 = 1 has no root in *U*, soon *V* = Ø.