LOGIC Flashcards
and
conjunction (^)
or
disjunction (v)
no
negation (~)
if p, then q
conditional / implication (->)
if and only if
biconditional (<->)
p exclusive or q
exclusive-or (O + cross)
true for all possible combinations of truth values
tautology
false for all possible combinations of truth values
contradiction
compound statement that can either be true or false
contingency
p v q = q ^ p
p v q = q v p
commutative
p ^ (q ^ r) = (p ^ q) ^ r
p v (q v r) = (p v q) v r
associative
p ^ (q v r) = (p ^ q) v (p ^ r)
p v (q ^ r) = (p v q) ^ (p v r)
distributive
p ^ t = p
p v F = p
identity
p ^ ~p = F
p v ~p = t
inverse
~ (~p) = p
double negation
p ^ p = p
p v p = p
idempotent
~ (p ^ q) = ~p v ~q
~ (p v q) = ~p ^ ~q
De Morgan’s law
p ^ F = F
p v t = t
universal bound
p ^ (p v q) = p
p v (p ^ q) = p
absorption
(p ^ q) -> r = p -> (q ->r)
exportation law
p -> q = ~q -> ~p
contrapositive
p -> q = (p ^ ~q) -> F
Reductio Ad Absurdum
p <-> q = (p -> q) ^ (q -> p)
p <-> q = (~p v q) ^ (p v ~q)
equivalence
p -> q = ~p v q
implication
