Section 2.2 Analyze Conditional Statements

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Presentation transcript:

Section 2.2 Analyze Conditional Statements

What is an if-then statement? If-then statements can be used to clarify statements that may seem confusing. These statements are logic statements. Logic statements are important in many different types of professions.

Examples: If the sun shines, then the grass will grow. If I live in NJ, then I live on the east coast. If the month is January, then next month is February.

These if-then statements are called conditional statements or conditionals. Conditional Statement: A logical statement that has two parts. In general, these conditionals are written: If p, then q or p q. Where p is the hypothesis and q is the conclusion.

Let’s take a look back at our examples: If the sun shines, then the grass will grow. If I live in NJ, then I live on the east coast. If the month is January, then next month is February.

Write the conditional statement in if-then form: The car will run if there is gas in the tank. I will wake up on time if my alarm goes off. If there is gas in the tank, then the car will run. If my alarm goes off, then I will wake up on time.

Converse: Exchange the hypothesis and conclusion of the conditional. The converse of p q is q p. Conditional: If I live in NJ, then I live on the east coast. Converse: If I live on the east coast, then I live in NJ. True! False!

The denial of a statement is called a negation. ~p represents “not p” 3.) This is geometry. This is not geometry. 4.) Today is not Thursday. Today is Thursday. 1.) An angle is obtuse. An angle is not obtuse. 2.) A puppy is a dog. A puppy is not a dog.

The inverse of a conditional can be formed by negating both the hypothesis and conclusion. ~p ~q If-then Statement: If you are from Mexico, then you speak Spanish. Inverse: If you are not from Mexico, then you do not speak Spanish.

Contrapositive: ~q ~p If-then statement: If you lift weights, then you will be strong. Contrapositive: If you are not strong, then you do not lift weights.

Quick Review If-then statement: If p, then q. Converse: If q, then p. Inverse: If ~p, then ~q. Contrapositive: If ~q, then ~p.

Let’s put it all together! If-then statement: If you live in Red Bank, NJ, then you live in Monmouth County. Converse: If you live in Monmouth County, then you live in Red Bank, NJ. Inverse: If you do not live in Red Bank, NJ, then you do not live in Monmouth County. Contrapositive: If you do not live in Monmouth County, then you do not live in Red Bank, NJ.