Preview of SL Logic Class 3. Either it is raining or it is snowing A A: It is raining B: It is snowing B  : Or 

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Presentation transcript:

Preview of SL Logic Class 3

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

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

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

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”

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

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… →

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

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

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)

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

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

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

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 

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

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

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