Consider the following two propositions.∀x∀y∀z((x 6 = y ∧ y 6 = z ∧ x 6 = z) → (¬P x ∨ ¬P y ∨ ¬P z))∃z(a = a → ∀yP y)(i) What is the maximum number of objects a model can have in its domain if both of the propositions are true on that model? Explain your answer.(ii) Give an example of a model that has the maximum number of objects in its domain and on which both of the propositions are true.

Give an example of a model (including domain, reference and extension) that has exactly two objects in its domain and on which all of the following four propositions are true.∃y∃x(x ≠ y ∧ Syxy) → ∀z(P z → Qz) ∀x∀y∀z(Sxyz ↔ (x = z ∧ y = a))∀x(Qx → x = b) a ≠ b ∧ (Qb ↔ ∃xSxbx)

Here is a model: Domain: {1, 2, 3, 4} B : {3, 4}, C : {1, 4}, F : ∅ Make a proposition that is false in this model by filling in each of the blank spaces of （blank)z((B（blank)（blank) z) → （blank)（blank)y¬F y) with one symbol of MPL. Explain why the proposition you made is false in the given model.

2. Here is a model: Domain: {1, 2, 3, 4} B : {3, 4}, C : {1, 4}, F : ∅ Make a proposition that is false in this model by filling in each of the blank spaces of _z((Bz _ _ z) → _ ∀ y¬F y) with one symbol of MPL. Explain why the proposition you made is false in the given model.

2. Here is a model: Domain: {1, 2, 3, 4} B : {3, 4}, C : {1, 4}, F : ∅ Make a proposition that is false in this model by filling in each of the blank spaces of _z((Bz _ _ z) → ¬∀ y¬F y) with one symbol of MPL. Explain why the proposition you made is false in the given model.

Let p and q be statements, and consider the following six statements.p ∧ ∼ q p ∨ q ∼ p ∧ q p → q q → p ∼ qDetermine the maximum number of these six statements that can be simultaneously true,and which truth values for p and q are needed to obtain this maximum. Explain yourreasoning.