For the following proposition, give the unique readability tree and the truth table derived from that tree. What type of statement (tautology, contradiction, satis able) is it? Why?
(p ! q) ! p ! p
2. Show the following logical equivalence using the logical identities and tautologies such as the law of the excluded middle.
(p ^ q) _ (p ^ s) _ (r ^ q) _ (r ^ s) (p _ r) ^ (q _ s)
3. Convert the following proposition to Conjunctive Normal Form. Show the steps required to get your answer.
(p $ q) ! (p ^ r)
4 Show the following using natural deduction.
no#(p → q) ` (r ∨ p) → (r ∨ q)
5 With the clauses given by Γ show Γ ` ¬r using resolution.
Γ = (p ∨ ¬q ∨ ¬r), (¬p ∨ s), (q ∨ ¬r ∨ t), (¬r ∨ ¬u ∨ t), (p ∨ s ∨ ¬r ∨ t), ¬s, q, u, (¬u ∨ ¬t)
o
6. Show a bottom up derivation of Γ ` h given the definite clauses (written as head ← body) in
set Γ.
7 Show a top down derivation of Γ ` h given the definite
set Γ.
6. Show a bottom up derivation of Γ ` h given the definite clauses (written as head ← body) in
set Γ.
7 Show a top down derivation of Γ ` h given the deficlauses (written as head ← body) in
6. Show a bottom up derivation of Γ ` h given the definite clauses (written as head ← body) in
set Γ.
