Quiz Logic Flashcards
p -> q ==
-p v q
Universal Quantification
“for all”, “for every”, “for each”
upsidedown A
Existential Quantification
backwards E
“for some”, “there exists”, “there is one”
Monotonic
in logic systems means can a truth ever be retracted
Converse (of an implication)
is obtained by reversing the roles of the premise and conclusion. Example p -> q becomes q -> p.
Inverse (of an implication)
is obtain by negating the premise and the conclusion. -p -> -q
Contrapositive of p -> q
-q -> -p
Converse, Inverse and Contrapositive of p -> q. Which are always equal?
Converse = q -> p
Inverse = -p -> -q
Contrapositive = -q -> -p
Contrapositive is equivalent to p -> q
Statements that are always true or false under the same conditions are called?
tautologies. example p->q == -p v q
Associative Law
(p v q) v r = ?
(p ^ q) ^ r = ?
(p v q) v r == p v (q v r) == p v (q v r)
or
(p ^ q) ^ r == p ^ (q ^ r)
Distributive Laws
p v (q ^ r) = ?
p ^ (q v r) = ?
p v (q ^ r) == (p v q) ^ (p v r)
or
p ^ (q v r) == (p ^ q) v (p ^ r)
De Morgan’s Laws
-(p ^ q) == -p v -q
or
-(p v q) == -p ^ - q
p <> q ==
(p -> q) ^ (q -> p)
or
(-p v q) ^ (-q v p)
Resolution and how it works?
method assumes that the premises are true and what we are trying to prove is false, and then try to find a contradiction. If we find a contradiction then the proof is true.
An expression is in clausal form if there is no
implication ( -> )
conjunction ( ^ )
double negation - (-)
Steps to convert to CNF?
- Remove Biconditional a b == (a -> b) ^ (b -> a)
- Remove Implication a -> b == -a v b
- Move Negation Inwards -(a v b) == -a ^ -b
or
-(a ^ b) == -a v -b
or
-(-a) == a - Apply Distribution and/or communitive law
a ^ (b v y) == (a ^ b) v (a ^ y)
or
a v (b ^ y) == (a v b) ^ (a v y)