Assume that P,Q,R,Z are complex well-formed formulas in the language of proposit

Question

Assume that P,Q,R,Z are complex well-formed formulas in the language of propositional logic. Next suppose a truth-tree test is used to determine if they are consistent or inconsistent, and the tree test produces a tree where all of the branches are closed. First, is the set of wffs {P,Q,R,Z} consistent or inconsistent? Second, what does a closed tree indicate about whether there is an interpretation (assignment of truth values to the propositional letters) that would make each wff in {P,Q,R,Z} true.

Explanation / Answer

answer:

(1) Inconsistent because all branches are closed.

There is no valuation where 'P,' 'Q,' 'R,' AND 'Z' are jointly true.

(2) A closed tree indicates that there is no way of consistently assigning truth valuesto propositional letters so that every proposition in the branch is true (including thosein the stack). Thus, there is no interpretation that would make P, Q, R, Z true.

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