Open Sentence in Math: Definition & Example

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  • 0:01 What Is an Open Sentence?
  • 0:46 Examples of Closed Sentences
  • 1:44 Examples of Open Sentences
  • 4:17 Lesson Summary
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Lesson Transcript
Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, you will learn the definition of an open sentence and will be given many examples to illustrate this concept. Following this lesson will be a quiz to test your new knowledge and skills.

What is an Open Sentence?

You were probably quite young when a teacher taught you about sentences and you learned that you needed a subject and a verb to make a sentence, like in these examples:

'The baby laughed.'

'The ocean is blue.'

In math, there are similar sentences with similar rules. A mathematical sentence makes a statement about two expressions. The two expressions either use numbers, variables, or a combination of both. A mathematical sentence can also use symbols or words like equals, greater than, or less than.

An open sentence in math means that it uses variables, meaning that it is not known whether or not the mathematical sentence is true or false.

A closed sentence, on the other hand, is a mathematical sentence that is known to be either true or false.

Examples of Closed Sentences

Before we look at open sentences, let's look at some examples of true closed sentences in math:

1. 9 is an odd number.

2. 4 + 4 = 8

3. 10 - 1 = 9

4. 6 - 6 = 0

5. The square root of 4 is 2.

If you notice, all of these sentences are true. Because we know they are true, they are closed sentences!

Let's look at some examples of false closed sentences in math:

1. 9 is an even number.

2. 4 + 4 = 5

3. 10 - 1 = 8

4. 6 - 6 = -1

5. The square root of 4 is 1.

Wow, it definitely did not feel right saying those mathematical sentences. Why? Because these mathematical sentences are completely false. We know that they are wrong. Therefore, they are false closed mathematical sentences.

Examples of Open Sentences

We get open sentences when we use variables in mathematical sentences.

Here are some examples:

1. The obtuse angle is N degrees.

2. X + Y = 5

3. 4 - 3 = X

4. A square has N sides.

5. 5 + Y = X

In the examples, the mathematical sentences or expressions may or may not be true depending on the values of the variables X, Y and N. These mathematical sentences simply lack the proper knowledge needed to know whether or not the expressions are true or false.

Let's take each example one at a time.

Example 1: The obtuse angle is 'n' degrees.

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