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Preview of SL Logic Class 3

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Either it is raining or it is snowing A A: It is raining B: It is snowing B : Or

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Sentence Letters: A, B, C….. A 1, A 2…

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Meet the Sentential Connectives! ~ Negation! & Conjunction! The Conditional! The Biconditional! Disjunction!

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The Connectives ~Negation. “Not” “~A” is read “Not A” &Conjunction. “And”. “A&B” is read “A and B” Disjunction. “Or” “A B” is read “A or B” Conditional. “If…then” “A B” is read “If A, then B” Biconditional “If and only if” “A B” is read “A if and only if B”

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I go to school and I have a job A A: I go to school B: I have a job B &: And &

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If my car breaks down, then I won’t be able to get to work A A: My car breaks down B: I won’t be able to get to work B →: If…then… →

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It is not the case that I will be able to get to work I won’t be able to get to work A A: I will be able to get to work ~: It is not the case that ~ I will be able to get to work

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If my car breaks down, then I won’t be able to get to work A: My car breaks down B: I will be able to get to work →: If…then… ~: Not A → ~B

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I will get to work if and only if my car works. A A: I will get to work B: My car works B ↔: If and only if ↔

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A: My car works B: I will go to work “I will go to work, if my car works’ A → B “I will go to work, only if my car works’ B → A “I will go to work if and only if my car works.” A ↔ B

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If it snows, school will be cancelled and we can build a snow fort.

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A: It snows B: School will be cancelled C: We can build a snow fort A → (B & C)

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It’s like arithmetic! Not the same! A → (B & C) (A → B) & C 1 + (2 × 3) = 7 (1 + 2) × 3 = 9

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All the elements of SL Sentence letters:A, B, C, A 1, B 234, … Sentential connectives: ~, &, , , Parentheses:(, )

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The sentential connectives are truth functional. They are defined by the way the transform the truth of the sentences they connect.

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Grass is green I am the Pope Either grass is green or I am the Pope. True False True T F becomes T F T

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The Parts of a Conditional A → B If A, then B Consequent Antecedent

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The Parts of a Conjunction A & B A and B Conjunct. Conjunct

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The Parts of a Disjunction A v B A orB Disjunct. Disjunct

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