What is Compound Inequality?
A compound inequality is an inequality that combines two simple inequalities by either the “AND” condition or the “OR” condition.
The compound inequality with “AND” tells us that the condition is true when all the conditions in the compound inequality are true. Sometimes we do not even require to write AND and but it is understood. As in 2<x<4 it is nowhere written AND condition but the meaning of the above condition is x>2 and x<4. AND is also called the intersection of the solution sets for the individual statements.
Whereas “OR” indicates that, as long as either of the one statement is true, the entire compound sentence is true. It is called the union of the solution sets for the individual statements.
We also called AND condition a Conjunction and OR condition a Disjunction. Let’s compare both of these conditions using the following table.
|
AND (Conjunction) |
OR (Disjunction) |
|---|---|
| In conjunction inequalities AND condition is used to join two or more inequalities. | In disjunction inequalities OR condition is used to join two or more inequalities. |
| Example of a conjunction is x > -1 AND x < 23 | Example of a disjunction is x < -1 OR x > -11 |
| This can be explained using the intersection of individual inequalities, for example in x > -1 AND x < 23 this can be expressed as, (-1, ∞) ∩ (-∞, 23). | This can be explained using the union of individual inequalities, for example in x < -1 OR x > -11this can be expressed as, (-∞, -1) ∪ (-11, ∞). |
| In this situation, the condition is true if all the individual conditions are true. | In this situation, the condition is true if either of the individual conditions is true. |
Compound Inequalities
Compound Inequalities are the combination of two or more inequalities. These inequalities are combined using two conditions that are AND, and OR. These conditions have specific meanings and they are solved differently. The inequities in compound inequalities are individually solved using normal rules but the combinations of their answers depend on the AND and OR conditions. So, let’s start learning about the concept of compound inequalities including their solutions and various other solved examples as well.