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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.

Sometimes, what is true in the mathematical world of logic is false in the real world. Check out this lesson to learn how to identify conditional statements and how you can differentiate between what is logically true and what is true in reality.

If I help you get an A in math, then you will give me ten thousand dollars. I like this statement. Do you? You might be laughing and saying to yourself 'yeah right,' but in the mathematical world of logic, this statement holds true just because of the way it is written. A statement like this is called a **conditional statement** because it has an if-then structure. All conditional statements say something like, 'If this happens, then that will occur.' Do you see how the statement I made to you earlier fits the if-then structure?

You can make conditional statements from anything you can think of as long as you have the if-then structure. Let's look at these examples.

If Carlos gets a car, then Lily's dog will be trained.

If Sam eats chocolate ice cream, then Judy eats double chocolate ice cream.

If a square is a rectangle, then a rectangle is a quadrilateral.

Notice how all of these are structured the same. All of them start with an 'if' part followed by a 'then' part.

The part after the 'if' and before the comma is called the **hypothesis**. This is the first part of a conditional statement. In my first statement, the hypothesis is, 'I help you get an A in math,' because this phrase comes between the 'if' and the comma. Can you spot the hypothesis in the other example of conditional statements? Yes, for the statement, 'If Carlos gets a car, then Lily's dog will be trained,' the hypothesis is, 'Carlos gets a car.' For the statement, 'If Sam eats chocolate ice cream, then Judy eats double chocolate ice cream,' the hypothesis is, 'Sam eats chocolate ice cream.' Can you locate the hypothesis for the statement, 'If a square is a rectangle, then a rectangle is a quadrilateral'?

You might be familiar with other definitions of the word hypothesis, but to help you remember what it is in math logic, just remember its location between the 'if' and the comma. Don't worry about what it means for now.

The second part of a conditional statement is the **conclusion**. It comes after the 'then' and before the period. 'You will give me ten thousand dollars' is the conclusion in my first statement. For the statement, 'If Carlos gets a car, then Lily's dog will be trained,' the conclusion is, 'Lily's dog will be trained.' And for the statement, 'If Sam eats chocolate ice cream, then Judy eats double chocolate ice cream,' the conclusion is, 'Judy eats double chocolate ice cream.' See if you can locate the conclusion in the statement, 'If a square is a rectangle, then a rectangle is a quadrilateral.'

Just like for the hypothesis, don't worry so much about the meaning of the word and just remember its location when dealing conditional statements. The conclusion is always between the 'then' and the period.

Also, when dealing with conditional statements, you have to set reality aside for a moment. Think about the statements, 'If Sue is pregnant, then she will give birth within the year' and 'If Sue is pregnant, then Sue's mom will give birth within the year.' Which makes more sense to you? Isn't it the first one? But, in the world of logic, if the first statement is labeled as false, then you have to stick with that. Likewise, if the second statement is labeled as true, you have to believe that, too. Whatever you are told is true or false, you have to believe that in the world of logic.

A key thing to remember here is that you can't think too hard about whether the statement is true in real life. Just read it, separate the conditional statement into its two parts and work with those. The statement could say the stupidest thing, but you have to treat it as true if it is marked as true. It might help to pretend you are not in the real world when working with conditional statements. Tell yourself that these conditional statements are rules for the imaginary world that you have entered where anything is possible.

In review, **conditional statements** have an if-then structure. They say something like, 'If this happens, then that will occur.' What the conditional statement says may sound ridiculous, but in the world of logic, you have to treat it as a true statement. A conditional statement is made up of two parts. The first part is the **hypothesis**, which comes after the 'if' and before the comma. The second part is the **conclusion**, which is after the 'then' and before the period. A conditional statement will look like 'if HYPOTHESIS, then CONCLUSION.'

Following this lesson, you should have the ability to:

- Define conditional statements in math
- Identify the two parts of a conditional statement
- Differentiate between logic and the real world when working with conditional statements in math

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Math 102: College Mathematics14 chapters | 108 lessons

- Critical Thinking and Logic in Mathematics 4:27
- Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice 4:47
- Logical Fallacies: Appeals to Ignorance, Emotion or Popularity 8:53
- Propositions, Truth Values and Truth Tables 9:49
- Logical Math Connectors: Conjunctions and Disjunctions 3:39
- Conditional Statements in Math 4:54
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