Logic

Translate the following into QL, being sure to provide a complete translation key.

2. No one is wiser than David.

3. There are at least two dishonest pirates.

5. If you harm someone, then someone else will harm you.

6. There is a barber who shaves all those barbers who don’t shave themselves.

Within the given model, determine the truth value of each of the following statements. In each case, briefly explain why you think the statement is true or false.

UD: {1, 2, 3, 4, 5, 6}

extension E: {2, 4, 6}

extension O: {1, 3, 5}

extension N: {Ø}

extension M: {1, 3, 6}

constant (p): 2

constant (q): 4

4. ∃x(Ox & Np) → ∀z(Ez v Mz)

Given the following premises, derive the conclusion.

Premises: (1) ∀x(Bx → ∀y(Ay → Cxy)), (2) Bj & ~Cjm, (3) ∃xDx

Conclusion: ~Am