Thẻ ghi nhớ: Semantics_Lecture 7_Propositional Logic | Quizlet

Propositional logic analyses certain ways of combining propositions to form

complex propositions

The expressions which are used to combine propositions are

the connectives: and, but, or, if, iff (if and only if)

The study of compound propositions and how their truth value is determined by the truth values of their constituent parts is known as

propositional logic

The truth value of a complex proposition formed with a truth functional connective can be calculated simply from

the truth values of the joined propositions

negation = not

~

not p = ~p

conjunction = and

^

p and q = p ^ q

disjunction = or

V

p or q = p V q

conditional = If...then...

-->

If p, then q = p --> q

biconditional = If and only if

<-->

P if and only if q = p <--> q

Alice didn't sleep

~SLEEP(a)

Truth table for negation

p T F

~p F T

Truth table for conjunction

p T T F F

q T F T F

p&q T F F F

p but q T F F F

Inclusive disjunction

either or both = V

Exclusive disjunction

either but not both = (+)

Truth table for disjunction

p T T F F

q T F T F

pVq T T T F

p(+)q F T T F

material implication connective

-->

Truth table for material implication

p T T F F

q T F T F

p-->q T F T T

Biconditional connective (Equivalence)

<-->

Truth table for equivalence

p T T F F

q T F T F

p<-->q T F F T