Appendix A
Always gives the opposite.
What is the rule of negation?
Simplification
What is:
when p . q is true,
p is true
Commutation
What rule states "for conjunction and disjunction, order doesn't matter"?
(p . q) = (q . p)
(p v q) = (q v p)
FREE POINTS
~~p
p
What is the Truth Tree Decomposition Rule for Double Negation (~~D)?
True when both are true.
What is the rule of Conjunction?
Conjunction
What is:
when p is true
and q is true,
then p . q is true
p = ~~p
Conjunction ( . D)
p . q
p
q
Negated Conjunction (~. D)
~(p . q)
/ \
~p ~q
False when both are false.
What is the rule of Disjunction?
p v q is true
What is the rule of addition?
[p . (q . r)] = [(p . q) . r]
[p v (q v r)] = [(p v q) v r]
What is the rule of Association?
Disjunction ( v D)
p v q
/ \
p q
Negated Disjunction
What Truth Tree Decomposition Rule states:
~(p v q)
~p
~q
What is the rule of a conditional?
If p then q
If q then r
Therefore, If p then r
What is a Hypothetical Syllogism?
(p > q) = (~p v q)
What is the rule of Material Implication?
p > q
/ \
~p q
What is the Truth Tree for Conditional (>D)?
~(p > q)
p
~q
What is the Truth Tree Decomposition Rule for a Negated Conditional (~>D)?
What is the rule of a biconditional?
Modus Ponens
What is:
If p then q
p
therefore, q
Tautology?
What rule states:
p = (p . p)
p = (p v p)
p = q
/ \
p ~p
q ~q
What is the Truth Tree Decomposition Rule for a Biconditional (=D)?
Negated Biconditional (~=D)
What Truth Tree Decomposition Rule States:
~(p = q)
/ \
p ~p
~q q