Logical symbols Flashcards
truth value
true or false assigned to a statement
proposition
a sentence that has a true or false truth value assigned to it
tautology
a proposition that is always true
contradiction (logic)
a proposition that is always false
~P
negation, “not P”
P ∨ Q
disjunction, “P or Q”
P ∧ Q
conjunction, “P and Q”
P => Q
“P implies Q”
P <= Q
“only if P, then Q”
P <=> Q
biconditional, “if and only if,” if you assume P is true, then Q is true; and if you assume Q is true, then P is true
∃
existential quantifier, “there exists”
∀
universal quantifier, “for all”
∈
“belongs to”
converse of P => Q
Q => P
contrapositive of P => Q
~Q => ~P
when are two statements equivalent (in logical statements)?
when their truth tables are equivalent
predicate
a statement that, given more information, becomes a propositon. EX: x^2 = 4
truth set
a collection of objects that makes a predicate true. EX: predicate is x^2 = 4, truth set is {2, -2}
what is “specifying the universe?”
specifying the number system we are working in
two quantified statements are equivalent if…
they have the same truth values in that universe
quantified statement
a statement containing “quantifiers” like “some,” “for all,” “there exists,” “none,” etc.
!
“unique”
