Question

2. Provide an example of a formula A such that U ⊨ A, where U is...

2. Provide an example of a formula A such that U ⊨ A, where U is the set of formulas given:

U = {¬p ∧ ¬ q, (p ∨ ¬q) ∧ ¬r, p → r}

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Answer #1

1. ¬p ∧ ¬ q

2. (p ∨ ¬q) ∧ ¬r

3. p → r

4. p ∨ ¬q [2 Simplification]

5. ¬q → p [4 using implication]

6. ¬q → r [5, 3 Disjunctive Syllogism]

Answer: ¬q → r

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