Rules of Inference
Modus Tollens
What Rule of Inference states:
p > q~q
~p
A conjunction can be distributed across a disjunction.
[p . (q v r)] = [(p . q) v (p . r)]
A disjunction can be distributed across a conjunction.
[p v (q . r)] = [(p v q) . (p v r)]
What does the rule of Distribution state?
True/False?
A disjunction can be distributed across a disjunction?
FALSE
A disjunction is false when p and q are false.
~(p v q) = (~p . ~q)
What does DeMorgan's Theorem State?
p v q
~p
q
What is a Disjunctive Syllogism?
True/False?
Rules of Replacement can be used within a larger proposition.
TRUE
A conjunction is false when p or q is false.
~(p . q) = (~p v ~q)
What does DeMorgan's Theorem State?
You can flip the constants in a conditional if you ~negate both.
What does the rule of Transposition state?
True or False: Rules of Inference can be used within a larger proposition.
FALSE
When a biconditional is true, the conditional is true is both directions.
What does the Rule of Material Equivalence state about conditionals?
Association
The Rule of Replacement that states:
For disjunction and conjunction grouping doesn't matter.
When a conditional is true, either p is false or q is true.
What does the Rule of Material Implication state?
p > q
p > (p . q)
What is the rule of Absorption?
In a biconditional, either p and q are both true or both false.
What does the Rule of Material Equivalence state about the truth value of biconditionals?
Material Implication
What rule of replacement states:
(p > q) = (~p v q)
True/False?
A conjunction can be distributed across a disjunction.
TRUE
Constructive Dillema
(p > q) . (r > s)
p > r
q > s
Exportation
[(p > (q > r)] = [(p . q) > r]
What rule of replacement states:
When the consequent of a conditional is a conditional, the antecedents can be expressed as a conjunction.
A compound statement that is always true.
What is Tautology?