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Math 102: College Mathematics14 chapters | 108 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how to identify conjunctions and disjunctions. Also learn the connectors that are used with each. Learn how you can use them to make statements.

Any time you say a phrase that can be labeled as either true or false, you are making a **statement**. If you said 'a triangle has three sides,' then you have stated a statement. Likewise, you would be making a statement if you said 'Sue has a Great Dane.' Both of these statements can be labeled as either true or false. Even though this is a math lesson, statements in general can be about anything at all.

When you have two statements and you want to combine them, you can add either an 'and' or an 'or' between the two statements. Each has a different meaning. Let's see what they are. We will also see how these connectors affect the combined compound statement in terms of labeling it as true or false.

When two statements are connected with an 'and,' you have a **conjunction**. For conjunctions, only when both statements are true is the combined compound statement true.

For example, if we had 'squares are rectangles' and 'circles are ovals' as our two statements, and we combined them with 'and' to make the compound statement 'squares are rectangles and circles are ovals,' this new compound statement is true only when the two statements we began with are true. If only one is true and the other is false, the compound statement is also false.

The same would be true if our two statements were 'John likes chocolate ice cream,' and 'Sue likes strawberry ice cream.' If we combined them with 'and' to make 'John likes chocolate ice cream, and Sue likes strawberry ice cream,' then the two statements must be true for the compound statement to be true.

A **disjunction**, on the other hand, is when two statements are connected with an 'or.' The combined compound statement in this case can be labeled as true when just one of the statements is true.

For example, if we had 'squares are rectangles or circles are ovals,' this compound statement is true when either the statement 'squares are rectangles' is true or 'circles are ovals' is true. Both of them do not have to be true at the same time for the compound statement to be true.

Likewise for the compound statement 'John likes chocolate ice cream, or Sue likes strawberry ice cream.' If the statement 'John likes chocolate ice cream' is true but the statement 'Sue likes strawberry ice cream' is false, then the compound statement is still true because of the 'or' connector.

Let's recap what we've learned. **Statements** are any phrase that can be labeled as either true or false. To combine two statements, we can add either an 'and' or an 'or' between the two statements to form a new compound statement.

When two statements are combined with an 'and,' you have a **conjunction**. For conjunctions, both statements must be true for the compound statement to be true. When your two statements are combined with an 'or,' you have a **disjunction**. For disjunctions, only one of the statements needs to be true for the compound statement to be true.

You could be able to do the following after studying this lesson:

- Recognize a statement
- Identify conjunction used to combine statements
- Emphasize the importance of connectors
- Point out the characteristics of a disjunction

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5 in chapter 11 of the course:

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Math 102: College Mathematics14 chapters | 108 lessons

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- Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice 4:47
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