CR Midterm Flashcards
& is TRUE
only when
Both of them are TRUE
v is TRUE when
all the time
except for
when both of them are False, then it is FALSE.
⊃ is TRUE when
BOTH of them are TRUE
or
1st FALSE and 2nd TRUE
Atomic Proposition
a proposition that doesn’t contain any other proposition as a component
ex: Yuna Kim is famous.
Songdo is in Korea.
≡ is true when
BOTH are True
or
BOTH are False
An argument is logically valid =def
it is impossible for all of the premises to be true and the conclusion false (in virtue of form and structure).
Compound / Complex Proposition
a proposition that is not ATOMIC
ex: Yonsei won 2-2 v Korea University won 2-1.
The scope
is the formulas that the connective applies to
in
P v Q
v is connective
P and Q are the scopes.
Main connective
the connective that has the widest scope in the formula.
Syntax
specifies the grammar of PL (propositional logic)
Semantics
give the meaning of ~, &, v, ≡, ⊃
by specifying EXACTLY WHEN they are TRUE.
Consistent Statements
there is at least 1 case when both of them are true at the same time
Inconsistent Statement
there is NO case when both of them are true at the same time
sometimes contradictory but not always
Contradictory Statements
are always INCONSISTENT
F. T
T. F
F. T
Logically Equivalent
Mirror image of each other
T. T
F. F
T. T
Not always consistent (when the whole column is F)
Tautology
Apply to only one wff (P) 1
(logical truth)
The whole column of the main connective is true
Self-contradictory
Applied to a wff
The whole column is FALSE
Consistent
applied to a wff
There is at least 1 truth.
Contingent
Applied to a wff
There is at least 1 TRUTH and 1 FALSE
If the conclusion is a tautology
the argument is always valid
because there is NO counter example (when the premises are T but the conclusion is F)
if we have a premise that is self-contradictory
the argument is ALWAYS valid
(there is no counter example)
it can never be SOUND
SOUNDNESS
an argument is VALID
and
ALL its PREMISES are TRUE
