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2-2 Logic

2-2 Logic. Ms. Andrejko. Real World. Legally Blonde. 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

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2-2 Logic

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  1. 2-2 Logic Ms. Andrejko

  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 CONJUNCTION NEGATION DISJUNCTION

  6. EXAMPLES - Find the truth value: • We are in room 604 • My name is Ms. Stoffers • Geometry is the 2nd 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 Statement: 60 seconds DOES NOT equal 1 minute, and congruent supplementary angles each have a measure of 90 2.~ p∨q 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 Statement: 60 seconds DOES NOT equal 1 minute, or -12 + 11 is not less than -1 2.~ p∨~r F ∨ T = T

  10. In your foldable… Negation Disjunction Conjunction

  11. Example - Complete the Truth Table F F F∨F = F F T F∨T = T T F T∨F = T T T T∨T = T

  12. Example - Complete the Truth Table F F ∧ T = F T F T F∧F = F T T∧ T = T F T T∧F = F T

  13. Example – Construct a truth table ~q ∧ r F F ∧ T = F F F∧F = F T∧ T = T T T T∧F = F

  14. Practice– Construct a truth table ~p∨r F F ∨ T = T F F ∨ F = F T T ∨ T = T T T∨ F = T

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