# I need to give formal proofs with first-order logic and translate English to FOL.

*label*Philosophy

*timer*Asked: Dec 13th, 2018

**Question description**

In each of the following, I need to assess whether the argument is valid. If it is, I need to give a formal proof with first-order logic. You may not use AnaCon nor TautCon. You must also simplify Modus Tollens and Modus Ponens, if necessary.

- ¬∀x (Cube(x) ∧ Small(x)) from the premise ¬∀x (Cube(x).
- ∃x ¬Cube(x) from the premises ∀x((Cube(x) ∧ Large(x)) → FrontOf(x,a)) and ∃x(Large(x) ∧ ¬FrontOf(x,a))
- ∀x∃y Smaller(x, y) from the premise ∃y∀x Smaller (x, y)

Second, I need to translate the sentences from English to first-order logic (Translation 1 file), and from first-order logic to English (Translation 2 file).