Definitions
This is a diagram that shows a set of propositions being decomposed into their literals.
What is a truth tree?
T or F: All branches must be open for the set to be consistent
What is false?
Don't forget to _____ the SM after is has been decomposed.
What is check off?
The conjunction rule states...
p * q
p
q
After completing a truth tree, the next step is to ______, or determine the truth values of the variables that would make the propositions consistent.
What is recover the truth values?
To break something down into its literals.
What is to decompose?
SM stands for _____
What is set member?
What is the fourth rule for constructing truth trees?
What is "decompose more complex propositions"?
The double negation decomposition rule states that...
--p
p
The negated conjunction decomposition rule states that...
-(p * q)
branch
-p, -q
What are literals?
A path on a truth tree for which a contradiction has been found.
What is a closed branch?
The third step for constructing truth trees.
What is "stop when the truth tree answers the question being asked" or "when an inconsistency is found"?
The disjunction decomposition rule states that...
p v q
branch
p, q
The negated disjunction decomposition rule states that..
-(p v q)
-p
-q
To determine the truth values of the simple propositions for which the propositions in the set would all be true.
What is to recover the truth values?
What is an open branch?
The second step for constructing truth trees.
What is "decompose members leading to closed branches"?
The biconditional decomposition rule states that...
p=q
branch
p, -p
q, -q
The negated conditional decomposition rule states that...
-(p>q)
p
-q
A truth tree can be used to determine the ______ of a set of propositions.
What is consistency?
What is true?
The first step for constructing truth trees.
What is "decompose non-branching members"?
The conditional decomposition rule states that...
p > q
branch
-p, q
The negated biconditional decomposition rule states that...
-(p=q)
branch
p, -p
-q, q