Agenda 10/6

1. Agenda10/6 • DO NOW: • There are three boxes. One is labeled "APPLES" another is labeled "ORANGES". The last one is labeled "APPLES AND ORANGES". You know that each is labeled incorrectly. You may pick one fruit from one box which you choose. How can you label the boxes correctly? • Finish discussion about the sum of the sequence from yesterday (2.1 notes) • Logical Statements and How to Analyze Them

2. Section 2.2An Introduction to Logic Geometry 2010 – 2011

3. Visual Models of Logic • Left is an Euler(pronounced “oiler”) diagram, a special type of Venndiagram. • It depicts the fact that all Corvettes are Chevrolets. • Write an “If-Then” statement.

4. Conditionals and Their Parts • A statement written in the form, “If p, then q,” is called a conditional. • In logical notation, the statement If p then q can be written symbolically as p => q. • This is read as “p implies q.” • The hypothesisis the phrase following the word if in a conditional. • The conclusionis the phrase following the word then in a conditional.

5. Let’s Apply It • Identify the hypothesis and the conclusion in the conditional you wrote in #2. • Now, consider the statement: • “Miss Wuchevich’s car is a Corvette.” Use your Euler diagram and deductive reasoning to make a conclusion about Miss Wuchevich’s car. Add Miss Wuchevich’s car to your Euler diagram in #1.

6. How do we name these processes? • Deductive reasoningis the process of drawing conclusions by using logical reasoning in an argument. • The converseof a conditional is the statement formed by interchanging the hypothesis and the conclusion of the original conditional. • Write the converse of the conditional you wrote in #2, “If a car is a Corvette, then it is a Chevrolet.” • If a car is a Chevrolet, then it is a Corvette. • Is this true or false? How do you know? • An example that proves a statement false, such as your example in #12, is called a counterexample.

7. What happens when conditionals are linked together? • A logical chain is a series of logically linked conditional statements. • Suppose you are given the conditionals If A then B, and If B then C. The If-Then Transitive Property states that you can conclude If A then C.

8. Arrange the statement below to form a logical chain. Then, write the conditional that follows from the logical chain. • If she makes sushi, then Miss Wuchevich burns the rice. • If Miss Wuchevich burns the rice, then she eats at Kiku (a Japanese restaurant). • If it is Miss Wuchevich’s night to cook, then she makes sushi. Figure http://en.wikipedia.org/wiki/File:Sushi.svg

9. EXIT SLIP • Draw a Euler diagram to illustrate the conditional “If it rains, then it is cloudy.” • What is the converse of the conditional you just wrote? Use your Euler diagram to illustrate whether the converse is true.

10. HOMEWORK • Page 94 • #7 – 12, 14 – 20 (even), 21 – 23, 24 – 38 (even), 39, 42 – 46, 47 – 50 • Be prepared to discuss INDUCTIVE REASONING (which is introduced in the homework)