Define Solution Set In Math

In this tutorial you ll learn the definition of a solution set and see an example.

Define solution set in math. A value or values we can put in place of a variable such as x that makes the equation true. 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. Means the null set or empty set. An example of a solution set is 0 1 and 2 for 4x 4 4.

A 3 7 9 14 b 9 14 28 such that. In mathematics a solution set is the set of values that satisfy a given set of equations or inequalities. The set can be defined by listing all its elements separated by commas and enclosed within braces. 5 2 7 is true so x 5 is a solution.

When x 10 the equation becomes the true statement. This is called the roster method. 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. When we put 5 in place of x we get.

V a e i o u b 2 4 6 8 10 x a b c d e however in some instances it may not be possible to list all the elements of a set. Solution sets for equations the set containing all the solutions of an equation is called the solution set for that equation. In the above discussion of empty sets we assumed that we were only looking for real solutions. 9 14 28 9 14 28 a b.

For example the equation x 6 4 has a solution 10. A b 9 14 a b. In mathematics a solution set is the set of values that satisfy a given set of equations or inequalities. We now need to make a couple of final comments before leaving this section.

5 2 7. This symbol is often called the empty 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 constraints. In solution set notation we say that the solution set is empty and denote it with the symbol.

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. I i f i 0. A x x x 0 a b. A collection of elements.

The definition of a solution set is the group of numbers that can satisfy an equation. X 2 7. Objects that belong to set a or set b. If an equation has no solutions we write for the solution set.

A is a subset of b. Set a is included in set b. Objects that belong to set a and set b. Solution sets solution sets for equations the set containing all the solutions of an equation is called the solution set for that equation.