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The solutions must be complete and easy to follow. Correct answers will not

yield full points without explanations as to how the answer was reached.

For each of the three problems, up to 5 points can be gained.1. Show that

(a) P → Q follows from P → Q ∧ R, and

(b) P ∨ Q follows from P ∨ R and R → P

with semantic tableaux. 2. Show that

(a) P → Q follows from P → Q ∧ R, and

(b) P ∨ Q follows from P ∨ R and R → P

with resolution. 3. Show that

(a) P → Q follows from P → Q ∧ R, and

(b) P ∨ Q follows from P ∨ R and R → P

with natural deduction.Home Exam 2, Derivations in propositional logic

Hand in at the latest 10 April 2023 23:59 CEST

The solutions must be complete and easy to follow. Correct answers will not

yield full points without explanations as to how the answer was reached.

For each of the three problems, up to 5 points can be gained.

1. Show that

(a) P → Q follows from P → Q ∧ R, and

(b) P ∨ Q follows from P ∨ R and R → P

with semantic tableaux.

2. Show that

(a) P → Q follows from P → Q ∧ R, and

(b) P ∨ Q follows from P ∨ R and R → P

with resolution.

3. Show that

(a) P → Q follows from P → Q ∧ R, and

(b) P ∨ Q follows from P ∨ R and R → P

with natural deduction.

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