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Preview of SL. Logic Class 3. A: It is raining. B: It is snowing. Either it is raining or it is snowing. : Or. A. B. . Sentence Letters: A, B, C….. A 1, A 2… . Meet the Sentential Connectives!. . . ~. Disjunction!. The Biconditional!. Negation!. &. . Conjunction!.
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Preview of SL Logic Class 3
A: It is raining B: It is snowing Either it is raining or it is snowing : Or A B
Sentence Letters: A, B, C….. A1, A2…
Meet the Sentential Connectives! ~ Disjunction! The Biconditional! Negation! & Conjunction! The Conditional!
I go to school and I have a job A: I go to school B: I have a job &: And A & B
If my car breaks down, then I won’t be able to get to work A: My car breaks down B: I won’t be able to get to work →: If…then… → A B
I won’t be able to get to work A: I will be able to get to work ~: It is not the case that ~ It is not the case that I will be able to get to work I will be able to get to work A
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
I will get to work if and only if my car works. A: I will get to work B: My car works ↔: If and only if ↔ A B
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
If it snows, school will be cancelled and we can build a snow fort.
A: It snows B: School will be cancelled C: We can build a snow fort A → (B & C) If it snows, school will be cancelled and we can build a snow fort.
Not the same! A → (B & C) (A → B) & C It’s like arithmetic! 1 + (2 × 3) = 7 (1 + 2) × 3 = 9
The sentential connectives are truth functional. They are defined by the way the transform the truth of the sentences they connect.
Grass is green True Either grass is green or I am the Pope. T T F becomes T F True I am the Pope False
The Parts of a Conditional If A, then B A → B Consequent Antecedent
The Parts of a Conjunction A and B A & B Conjunct. Conjunct
The Parts of a Disjunction A orB A v B Disjunct. Disjunct