PHI 113 UC Davis Derivations and Definability Questions Metalogic assignment. Involving derivation and definability. Assignment in Attachment. Assignment #

PHI 113 UC Davis Derivations and Definability Questions Metalogic assignment. Involving derivation and definability. Assignment in Attachment. Assignment #2:
Derivations and Definability
phi113 Metalogic
Due: Friday, 5th of June
This assignment consists of three questions, and is worth 25% of your final grade.
Question 1:
Show that derivations exist for the following arguments.
1. ` ∀x¬A(x) → ¬∃xA(x)
2. ` ¬∀xA(x) → ∃x¬A(x)
You may find it particularly helpful to appeal to the following derived rules
A → (B → C) ` B → (A → C);
A → B, B → C ` A → C
Question 2: Let L< be the language containing a 2-place predicate symbol < only (no other constant symbols, function symbols, or predicate symbols other than =). Let N be the structure where |N| = N, and Purchase answer to see full attachment