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.
- 1. ¬?x (Cube(x) ? Small(x)) from the premise ¬?x (Cube(x).
- 2. ?x ¬Cube(x) from the premises ?x((Cube(x) ? Large(x)) ? FrontOf(x,a)) and ?x(Large(x) ? ¬FrontOf(x,a))
- 3. ?x?y Smaller(x, y) from the premise ?y?x Smaller (x, y)
Translate the sentences from English to first-order logic (Translation 1 file), and from first-order logic to English (Translation 2 file).