University College London Logical Questions Response

Overview

1. Suppose that P and Q are statements of the propositional language PROP. Prove that if PI=¬Q then QI=¬P.

2.Suppose that P, Q, and R are statements of the propositional language PROP. Prove that if PI=(QvR) and PI=¬Q then PI=(P→R).

3.Explain what it is for a tree-rule of PROP to be correct (or, what means the same thing, for it to be rule-correct). Demonstrate that the tree-rules that you learned for statements of PROP of the form '(P∧Q)' and '¬(P∧Q)' are correct.

4.Suppose that P₁, ..., P_n are some statements of PROP. Given that {P₁, ..., P_n} is an consistent (equivalently, unsatisfiable) set, can there be a closed and finished tree that starts with P₁, ..., P_n? Justify your answer.