In this assignment, your task is to find multiple models for each set of formulas and to write each model in Python. Each model should include (1) the domain of discourse, which must be integers; and (2) the extensional definition of the predicates, which are the tuples that make it true. For example: domain = {0,1,2} P = {(0,1), (1,2)} # Assuming P takes 2 arguments (e.g., P(x,y)) Q = {(0), (2)} # Assuming Q takes 1 argument (e.g., Q(x)) R = {} Your predicates may be the empty set, but your domain of discourse needs at least one element. Write your answers (using the above syntax) as your response to this assignment. The questions should be numbered 1a, 1b, etc. Your formulas for this assignment are available as logical formulas here and as Python code here F1 ∀z.(∀x.S(z,x)→¬∃x.S(z,x)) F2 (∀y.∀x.P(y,x)∨∀y.(¬∃x.P(y,x)→¬T(y))) F3 (∃x.P(x)∧∀x.(P(x)∧∃y.S(x,y))) F4 (∀x.(P(x)→∀y.S(x,y))∨∀x.∀y.S(x,y))

Question 1 (2pt) Given formulae F3 and F4 find:

a. A model that satisfies F3 but not F4

b. A model that satisfies F4 but not F3

c. A model that satisfies both F3 and F4

d. A model that doesn't satisfy either F3 or F4 Question

Q2. Propose and solve a question to test predicate semantics that is a completely different form than the one above (i.e., a question that doesn't just ask you to come up with a model to evaluate to T/F).