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Preview of SL

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

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  1. Preview of SL Logic Class 3

  2. A: It is raining B: It is snowing Either it is raining or it is snowing : Or A B 

  3. Sentence Letters: A, B, C….. A1, A2…

  4. Meet the Sentential Connectives!   ~ Disjunction! The Biconditional! Negation! &  Conjunction! The Conditional!

  5. The Connectives

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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

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

  13. 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.

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

  15. All the elements of SL

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

  17. 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

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

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

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

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