Solution Set Meaning In Math

For example for a set f i displaystyle f i of polynomials over a ring r displaystyle r the solution set is the subset of r displaystyle r on which the polynomials all vanish formally x r.

Solution set meaning in math. In sets theory you will learn about sets and it s properties. In mathematics a solution set is the set of values that satisfy a given set of equations or inequalities. If the solution set is a range of numbers as the one we looked at above is we will use something called set builder notation. Depending on the complexity of the inequality the solution set may be a single number or it may be a range of numbers.

A value or values we can put in place of a variable such as x that makes the equation true. X 2 7. When an equation has two variables the set of ordered pairs that are the solution to the equation are called the solution set to the equation. Solution set definition the solution set for an equation is the set of all number s that when used in the place of the variable makes the equation a true statement.

Symbols save time and space when writing. 5 2 7. Set subset union intersection element cardinality empty set natural real complex number set. Displaystyle x in r forall i in i f i 0 the feasible region of a constrained optimization problem is the solution set of the.

When x 10 the equation becomes the true statement. A set is a collection of things usually numbers. For example the equation x 6 4 has a solution 10. In this tutorial you ll learn the definition of a solution set and see an example.

When we put 5 in place of x we get. Common symbols used in set theory. If it is a single number then we use the same notation as we used for equations. We can list each element or member of a set inside curly brackets like this.

Also check the set symbols here. I i f i 0. In mathematics a solution set is the set of values that satisfy a given set of equations or inequalities. For example for a set of polynomials over a ring the solution set is the subset of on which the polynomials all vanish evaluate to 0 formally.

5 2 7 is true so x 5 is a solution.