Conditional Statements in Math

Logical Equivalence: Converse, Inverse, Contrapositive & Counterexample

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. Watch this video lesson to learn how to identify conditional statements and how you can differentiate between what is logically true and what is true in reality.

What Are Conditional Statements?

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 Hypothesis

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 Conclusion

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.

Source: study.com

Category: Forex

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