LOGIC CONNECTIVES AND MORE CONNECTIVES Group members Annisa

LOGIC CONNECTIVES AND MORE CONNECTIVES Group members: Annisa dwi lestari (1505085043) Novira anjani (1505085044) Agustina (1505085074) Gusti ahmad firdaus (1505085045) (absent/ not participate in presentation)

Connectives: and AND or

CONNECTIVES Provide a way of joining simple propositions to form complex propositions • Function: as a connector between two simple propositions that has truth value

AND • Symbolized with “&” in notation proposition • It is called conjunction • Only propositions can be connected with “&” (predicates and names cannot be connected with “&”)

EXAMPLE Andy Entered Mary Left a ENTER & m LEAVE For more than two propositions Caesar came to Gaul c COME g Caesar saw Gaul c SEE g Caesar conquered Gaul c CONQUER g (c COME g) & (c SEE g) & (c CONQUER g)

Joining compound propositions Ex: Adolfo and Benito are Italian a ITALIAN & b ITALIAN Commutativity of conjunction formed new complex proposition that equivalent with the previous proposition Ex: Agnes invite Marya and Agnes invite Rose a INVITE m & a INVITE r equivalent a INVITE r & a INVITE m

OR • Symbolized with “V” (latin: vel) • This is called disjunction Ex: Dorothy saw Bill d SEE b Dorothy saw Alan d SEE a (d SEE b) V (d SEE a)

Commutativity of disjunction formed new complex proposition that equivalent with the previous proposition Ex: Dorothy or Bernard saw Rose d SEE r V b SEE r equivalent b SEE r V d SEE r

RESOLVING AMBIGUITY • Placing either Ex: Alice went to Birmingham and she met Cyril or she called on David. Two meaning can be expressed a GO b & (a MEET c V a CALL-ON d) OR (a GO b & a MEET c) V a CALL-ON d

a GO b & (a MEET c V a CALL-ON d) Alice went to Birmingham and either she met Cyril or she called on David (a GO b & a MEET c) V a CALL-ON d Either Alice went to Birmingham and she met Cyril or she called on David

INFERENCE • To know the truth value between premiss and conclusion

In a situation in which Harry died and Terry resigned Truth Table For “&” Truth Table For “V” p T T F F q T F p&q T F F F P and q is true only when both p and q are both true q T F p. Vq T T T F P and q is true if one or both p and q is true

TRUTH VALUE OF COMPLEX PROPOSITION ((j BEHIND e) & (r SMILE)) V (e STAND) T V ((j BEHIND e) & (r SMILE)) T & T T (j BEHIND e) r SMILE F e STAND

More Connectives: negation, implication, and biconditional

Negation (~ ) • the connective ~ used in propositional logic is paraphrasable as English not. • Negation does not connect propositions, as do & and V

Example of Negation (~) • Alice didn't sleep the formula : ~ a SLEEP Claire is not between Edinburgh and Aberdeen the formula : ~ c BETWEEN e a

Implication (→) • The logical connective symbolized by → to the relation between an `if` clause and its sequel in English • Example if Alan is here, Clive is a liar the formula : a HERE → c LIAR

Biconditional (≡) • Biconditional is expresses the meaning of if and only if in English. Example Ada is married to Ben if and only if Ben is married to Ada the formula : (a MARRY b) ≡ (b MARRY a)

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