Chapter 6 Self Test
1. Define:
a. Soundness of the tree method
b. Consistency of the tree method
c. Extensionality of the sentences of SL
d. Completeness of SD
2. Choose the best answer:
The basic idea behind proving the completeness of the tree method is proving:
a. That if all the set members on the top of the tree for a set, Γ, of sentences of SL are
true on a truth value assignment, α, then all the sentences along at least one branch
of the tree for Γ must be true on α.
b. That if all the literals on the completed open branch of the tree for Γ are true on a truth
value assignment, α, then all the set members on the top of the tree must be true on
α.
c. That the tree for any finite set, Γ, of sentences of SL will either close or produce a
completed open branch after a finite number of steps.
d. That if Γ is a truth functionally inconsistent set containing infinitely many sentences of
SL, then there is a finite subset of Γ that is truth functionally inconsistent.
e. That for any sentence, P, of SL, {P} and {~P} could not both have closed trees.
3. Specify the length of the following sentences and explain how the notion of the length of a
sentence figures in establishing an important metatheoretic result.
a. ~~A
b. ~A v B
4. Suppose that a tree branch, θ, has sentences on it that are all true on a truth value
assignment, α. Sho

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