Unit 2 Logic Theory 2 3 Conditionals and

Unit 2 – Logic Theory 2. 3 Conditionals and Biconditionals

What happens when you get angry… • Let’s take a look at what may happen when you get angry! Don’t wind up in a ditch!!!!

Think about this statement again… • Consider the true statement from Tuesday: “ If I give you an “A” for your grade, then you will pass this class. What happens if you don’t get an A? ” This type of statement is called a conditional statement.

Symbols and language to represent Logic Theory and Set Theory Logic Theory Language Symbol and or not Set Theory Language Set Theory Symbol intersecti on union complem ’

What are conditional statements? • Conditional statements are as common in everyday language as they are in mathematics and logic. i. e. “If the seal is broken, then the product cannot be returned. ” “If you are not 48 inches tall, then you cannot ride this roller coaster. ” • Everyday examples of conditional statements. • There is only one way a conditional statement can be false…let’s take a closer look.

Example 1: •

Example 1 cont. Case 1: (w is true and b is true): You come to work and you will receive the bonus. Case 2: (w is true and b is false): You come to work and you don’t receive the bonus. Case 3: (w is false and b is true): You don’t come to work, but Mr. Rich gives you the bonus anyway. Case 4: (w is false and b is false): You don’t come to work and you don’t receive the bonus.

Definition: • p q T T F F T F T T

Example 2: • A boutique has the following policy: If you return clothing within 30 days with the original labels on it, then you will be given a full refund on your purchase. Shandra returned her suit with its original labels, but she was not given a refund. What can we deduce from this information?

Solution: •

Converse, Inverse, and Contrapositive •

Rewriting Statements in If …. Then Form Write the following statements in if …. then form: a) Your driver’s license will be suspended if you are convicted of driving under the influence of alcohol. b) In order to hold your room reservation, it is sufficient to give us your credit card number. c) In order to qualify for a discount on your airline tickets, it is necessary to pay for them two weeks in advance.

Solutions: a) If you are convicted of driving under the influence of alcohol, then your driver’s license will be suspended. b) If you give us your credit card number, then [we will] hold your room reservation. c) If you qualify for a discount on your airline tickets then you pay for them two weeks in advance.

Biconditionals • p q T T F F F T

What are your questions, what questions do you have?

Checking for Understanding: • While watching this video on Conditional Truth tables, write down three “I notice or I wonder” statements. • Complete the Truth Tables with Conditionals assignment for today that has been uploaded in google classroom.

Pg. 107 (#s 1 - 8) Pg. 108 (#s 21 – 27)