Lesson 2-2.A Logic: Venn Diagrams

Standardized Test Practice: Transparency 2-2 5-Minute Check on Lesson 2-1 Make a conjecture about the next item in the sequence. 1. 1, 4, 9, 16, 25 2. 2/3, 3/4, 4/5, 5/6, 6/7 Determine whether each conjecture is true or false. Give a counterexample for any false conjecture. Given: ABC with mA = 60, mB = 60 and mC = 60. Conjecture: ABC is equilateral. 4. Given: 1 and 2 are supplementary angles. Conjecture: 1 and 2 are congruent. 5. Given: RST is isosceles. Conjecture: RS  ST 6. Make a conjecture about the next item in the sequence: 64, –32, 16, –8, 4. Standardized Test Practice: A –4 B –2 C 2 D 4

Standardized Test Practice: Transparency 2-2 5-Minute Check on Lesson 2-1 Make a conjecture about the next item in the sequence. 1. 1, 4, 9, 16, 25, 36 2. 2/3, 3/4, 4/5, 5/6, 6/7, 7/8 Determine whether each conjecture is true or false. Give a counterexample for any false conjecture. Given: ABC with mA = 60, mB = 60 and mC = 60. Conjecture: ABC is equilateral. True 4. Given: 1 and 2 are supplementary angles. Conjecture: 1 and 2 are congruent. False; m1 = 70, m2 = 110. 5. Given: RST is isosceles. __ __ Conjecture: RS  ST False; RS  RT 6. Make a conjecture about the next item in the sequence: 64, –32, 16, –8, 4. Standardized Test Practice: A –4 B –2 C 2 D 4

Objectives Determine truth values of conjunctions and disjunctions Construct and interpret Venn diagrams

Vocabulary And symbol () Or symbol () Not symbol (~) Statement – any sentence that is either true or false, but not both Truth value – the truth or falsity of a statement Negation – has the opposite meaning of the statement, and the opposite truth value Compound statement – two or more statements joined together Conjunction – compound statement formed by joining 2 or more statements with “and” Disjunction – compound statement formed by joining 2 or more statements with “or”

Venn Diagrams P: All students at Marion Senior High School Q P ٨ Q P: All students at Marion Senior High School Q: All students born in Virginia P ٨ Q: All students at Marion SHS and were born in Virginia P: All students at Marion Senior High School Q: All students born in Virginia P ٧ Q: All students at Marion SHS or were born in Virginia P ٧ Q

DANCING The Venn diagram shows the number of students enrolled in Monique’s Dance School for tap, jazz, and ballet classes.

How many students are enrolled in all three classes? The students that are enrolled in all three classes are represented by the intersection of all three sets. Answer: There are 9 students enrolled in all three classes Example 2-3a

How many students are enrolled in tap or ballet? The students that are enrolled in tap or ballet are represented by the union of these two sets. Answer: There are 28 + 13 + 9 + 17 + 25 + 29 or 121 students enrolled in tap or ballet.

How many students are enrolled in jazz and ballet and not tap? The students that are enrolled in jazz and ballet and not tap are represented by the intersection of jazz and ballet minus any students enrolled in tap. Answer: There are 25 + 9 – 9 or 25 students enrolled in jazz and ballet and not tap.

PETS The Venn diagram shows the number of students at Manhattan School that have dogs, cats, and birds as household pets.

a. How many students in Manhattan School have one of three types of pets? b. How many students have dogs or cats? c. How many students have dogs, cats, and birds as pets? Answer: 311 Answer: 280 Answer: 10

Summary & Homework Summary: Homework: Day 1: pg 72: 4-17 Negation of a statement has the opposite truth value of the original statement Venn diagrams and truth tables can be used to determine the truth values of statements Homework: Day 1: pg 72: 4-17 Day 2: pg 72-3: 18, 19, 25, 26, 35-38, 41-44