Logic 1, WS 2007. Homework 1, given Oct 11, due Oct 18

1. Prove by definition that for any propositional formulae ϕ_{1}, …, ϕ_{n}, ψ: if the formula ϕ_{1} ∧ … ∧ ϕ_{n} ⇒ ψ is valid, then ϕ_{1}, …, ϕ_{n} ⊧ ψ.

2. Compute the truth value of the formula (A ∨ B) ⇒ C and compare the semantic function with the semantic function of the formula (A ⇒ C) ∧ (B ⇒ C) (which was computed during the lecture).

3. Give equivalent formulae for all logical connectives when one of the operands is 𝔽.

4. (optional) Give a formal proof of the correctness for the resolution inference rule.

5. Find the truth value of ∨∅ (the empty disjunction).