is the study of reasoning
logic
is a declarative sentence that is either true or false, but cannot be both at the same time
Statement
one that is neither true or false
Open statement
is a statement that expresses a single idea
Simple statement
can be formed by joining statements p and q
Compound statement
∧
and
∨
or
⟹
implies
⟺
if and only if
~
not (negation)
words all, each, every, some, no, and none.
quantifier
a statement that uses a quantifier
Quantified statement
some, for some, there exists, at least one
Existential quantifiers
∃
there exists
no, none, all, every, for all, for every
Universal quantifiers
∀
for all
Negation for All X are Y
Some X are not Y
Negation for Not X are Y
Some X are Y