CONNECTIVES:and ANDor

Riana Wieke Adiningtyas

Connectives ‘and’ (&) Logical conjunction

Caesar come to Gaul c COME gCaesar saw Gaul c SEE gCaesar conquered Gaul c CONQUER g(c COME g) & (c SEE g) & (c CONQUER g)

Andy entered and Mary lefta ENTER & m LEAVE

John loves Mary and Mary loves Billj LOVE m & m LOVE b

John and Mary are Irishj IRISH & m IRISH

Commutativity of Conjunction

God punished Adam and EveGod punished Eve and Adam

p & q (premiss)q & p (conclusion)

Melanie is pregnant and Mike is in BelgiumMike is in Belgium and Melanie is pregnant

Lorna left and Bill stayed.Lorna left

Frances sang and Harry tapdanced.Harry tapdanced

p & qq & p

p & q p

p & q q

Truth Table for &

1) Henry died and Terry resigned are both true, is Henry died and Terry resigned true or false?

2) Hendry died is true, but Terry resigned is false, is Henry died and Terry resigned true or false?

3) Henry died is false, but Terry resigned is true, is Henry died and Terry resigned true or false?

4) Henry died and Terry resigned are both false, is Henry died and Terry resigned true or false?

p q

T T

T F

F T

F F

p & q

T

F

F

F

Connectives ‘or’ (V) Logical disjunction

Harry is here h HERECharlie is a Dutchman c DUTCHMAN(h HERE) V (c DUTCHMAN)

Dorothy saw Bill or Aland SEE b V d SEE a

Either Dunfermline or Kirkcaldy is the capital of Fifed CAPITAL f V k CAPITAL f

Bernard or Christine strangled MaryChristine or Bernard strangled Mary

p V q (premiss)q V p (conclusion)

Truth Table for V

1) Henry died and Terry resigned are both true, is Henry died or Terry resigned true or false?

2) Hendry died is true, but Terry resigned is false, is Henry died or Terry resigned true or false?

3) Henry died is false, but Terry resigned is true, is Henry died or Terry resigned true or false?

4) Henry died and Terry resigned are both false, is Henry died or Terry resigned true or false?

p q

T T

T F

F T

F F

p V q

T

T

T

F

Alice went to Birmingham and she met Cyril or she called on David.

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

2) 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)

Adam will take Lucy or Cathy and Diana.(a TAKE l V a TAKE c) & a TAKE da TAKE l V (a TAKE c & a TAKE d)

o SMILEmi SITma CURLYs STAND

o SMILE {T} ma CURLY {T} s SIT {F}

(o SMILE) & (ma CURLY) {T}

((o SMILE & ma CURLY)) V (s SIT) {T}

Compositionally of Meaning

The meaning of any expression is a function of the meanings of the parts of which is composed.

Truth values of complex propositions are derived from the truth values of their constituent simple propositions.

The truth tables we have given for & and V are in fact functions of the kind mentioned in this definitions.