1. Ms. Andrejko 2-2 Logic

2. Real World Legally Blonde

3. Vocabulary Statement-a sentence that is either true or false Truth Value- the truth value of a statement must either be true or false Negation- the statement takes on the opposite meaning and opposite truth value Compound statement- two or more statements joined by the word and or or. Conjunction- a compound statement using the word and Disjunction- A compound statement that uses the word or. Truth table- used to determine truth values of negations and compound statements

4. Notations AND OR NEGATION

5. TRUTH TABLES p~p TF FT pq p ∧qp ∧q TTT TFF FTF FFF pq p∨qp∨q TTT TFT FTT FFF NEGATION CONJUNCTION DISJUNCTION

6. EXAMPLES - Find the truth value: We are in room 604 My name is Ms. Stoffers Geometry is the 2 nd course in the HS math sequence, and it is snowing outside ~(We have an ocean in Arizona) A dog is a mammal or a bird is an amphibian TRUE FALSE TRUE & FALSE = FALSE TRUE TRUE or FALSE = TRUE

7. PRACTICE- Find the truth value: June has 30 days There are 14 months in a year SDOH’s colors are blue and gold and SDOHS’s mascot is a tiger ~(The Cardinals are the home football team to Detroit) Phoenix is the capital of Arizona or Arizona State University’s mascot is a wildcat. TRUE FALSE TRUE & FALSE = FALSE TRUE TRUE or FALSE = TRUE

8. Examples Use the following statements to write a compound statement. Then find it’s truth value: p: 60 seconds = 1 minute q: Congruent supplementary angles each have a measure of 90 r: -12 + 11< -1 1. p ∧ q Statement: 60 seconds equals 1 minute, and congruent supplementary angles each have a measure of 90 T ∧ T = T 2.~ p ∨ q Statement: 60 seconds DOES NOT equal 1 minute, and congruent supplementary angles each have a measure of 90 F ∨ T = T

9. Practice Use the following statements to write a compound statement. Then find it’s truth value: p: 60 seonds = 1 minute q: Congruent supplementary angles each have a measure of 90 r: -12 + 11< -1 1. q ∨ r Statement: Congruent supplementary angles each have a measure of 90 or -12 + 11 < -1 T ∨ F = T 2.~ p ∨ ~r Statement: 60 seconds DOES NOT equal 1 minute, or -12 + 11 is not less than -1 F ∨ T = T

10. In your foldable…

11. Example - Complete the Truth Table pq~p~q ~p ∨ ~q TT TF FT FF FF FT TF TT F ∨ F = F F ∨ T = T T ∨ F = T T ∨ T = T

12. Example - Complete the Truth Table pq~p ~p ∧ q~(~p ∧ q) TT TF FT FF F F ∧ T = F F T T F ∧ F = F T ∧ T = T T ∧ F = F T T F T

13. Example – Construct a truth table qr~q ~q ∧ r TT TF FT FF F F ∧ T = F F T T F ∧ F = F T ∧ T = T T ∧ F = F ~q ∧ r

14. Practice– Construct a truth table pr~p ~p ∨ r TT TF FT FF F F ∨ T = T F T T ~p ∨ r F ∨ F = F T ∨ T = T T ∨ F = T