Logic Flashcards
P then Q
P
Therefore Q
Modus Ponens
P then Q
~Q
Therefore ~P
Modus Tollens
P then Q
Q
Therefore P
Converse Error
P then Q
~P
Therefore ~Q
Inverse Error
~P then C
Therefore P
Contradiction Rule
P
Therefore P or Q
Generalization Rule
P and Q
Therefore P
Specialization Rule
P
Q
Therefore P and Q
Conjunction Rule
P or Q
~Q
Therefore P
Elimination
P then Q
Q then R
Therefore P then R
Transitivity Rule
P or Q
P then R
Q then R
Therefore R
Proof by Division into Cases
Distribute:
P and (Q or R)
(P and Q) or (P and R)
What Laws are these?
P and t = P
P or c = P
Identity Laws
What law is this?
P or ~P = t
Negation Law
What laws are these?
P and P = P
P or P = P
Idempotent Laws
What Laws are these?
P or t = t
P and c = c
Universal bound Laws
What law is this?
P or (P and Q) = P
Absorption Law
Negation of Conditional Statement
If P then Q
P and not Q
The only way for “if P then Q” to be false is if P happened and Q did not.
Contrapositive of Conditional Statement
If P then Q
If not Q then not P
This is equivalent to the Conditional Statement
Converse of Conditional Statement
If P then Q
If Q then P
Inverse of Conditional Statement
If P then Q
If not P then not Q
Convert to Boolean logic
R is a sufficient condition for S
If R then S
Convert to a Boolean expression
R is a necessary condition for S
R if, and only if, S
