5 Axiomatisation of the Vegetables and Toys CompetitionAll entries to this competition must strictly obey all formulae in a set of traditional axioms,otherwise they will be disqualified. The axioms should be interpreted according to the followingspecification (key):Domain of discourse:All items on the tea trayV(2)Item a is a vegetableT(z)Item z is a toyB(x, y)Item a is balanced on item y.Notes:• The possible numbers of entities in the domain is not specified explicitly, but may berestricted by the axioms that must be satisfied.• The tea tray itself is not in the domain of discourse. Thus the axioms only apply to the itemson the tray, not the tray. It is required that a single tea tray is used, satisfying British tea trayregulations and appropriate standards of taste and decency. It should preferably be a familyheirloom.• The category of vegetable also includes so-called "fruit" -- tomatoes and cucumbers arewelcome, and of course rhubarb. For the real competition, the fruit must have been grown bythe contestent but we ignore this in the present axiomatisation.• The category of toy includes any toy-like individual item. Prizes are most likely to be awardedfor arrangements involving knitted toys made by the contestant, but this is not a strictrequirement.Rule AxiomRule Name1. Vz[V(x)V T(x))Essential Ontological Precondition2. B3y3z[V(x) ^ V (y) A-(2 = y) A T(z)]Rule of PlentyVæVyVzvw[ (V(x) A V(y) A V (2) A V(w))+ (x = y Vr = z Va = w Vy = z V y = w V z = w) ]3.Yorkshire Rule of Parsimony4. -3æ(V (z) A T(x)]Requirement of Good Taste 5. Vz[T(x) + 3y[V (y) ^ B(x, y)]]Superiority Mandate-Ba3y3v[ T(x) A T(y) A-(2 = y)6.Each to their ownΛ Β(π, υ) Λ (ψ, υ]7. -3a3y[B(x,y) ^ B(y, x)]Balancing Principle 18. Vævyvz[(B(x, y) ^ B(y, z)) → ¬B(x, z)]Balancing Principle 29. -3Jy3z3w[B(x, y) ^ B(y, z) A B(z,w)]Health and Safety10. -3a3yaz(¬(y = z) A B(x, y) A B(x, z)]The 'no straddling' rule - peculiar to Otley11. Jarvy[ Vz[¬B(y, z)] + (y = x) ]Foundational Structural LawAn arrangement of vegetables and toys that satisfies all of these axioms will be called a legalarrangment.General guidelines for the following questions• The following questions are a mixture of multiple choice and multiple selection questions.• In the multiple choice questions the possible answers are preceded by circular buttons. Youmust chose exactly one option from those avalable.• In the multiple selection quetions the possible answers are preceded by square tick boxes.You must chose all correct options. The correct answer could be any selection (includingnone or all) from the option.What is the minimum number of toys allowed in a legal arrangement?01O 2O 34O 5

Solution:-- 1)The given question is an type of the multiple choice question as it has been…

5. Vz[T(x) → 3y[V (») ^ B(z, y)]] Superiority Mandate -33y30[ T(x) ^ T(y) ^ -(z = y) A B(z, v) A B(y, v)] 6. Each to their own 7. -33y(B(z,y) A B(y, z)] Balancing Principle 1 8. Vzvyvz[(B(x,y) A B(y, z)) → -B(z, 2) Balancing Principle 2 9. -J3y3z3w[B(x, v) ^ B(y, z) ^ B(z, w)] Health and Safety 10. -33y3z|¬(y = z) ^ B(z,y) ^ B(z, z)] The 'no straddling' rule - pecullar to Otley [(2 = 6) ++ [(z 'f)g-]zA ]MAZE W Foundational Structural Law An arrangement of vegetables and toys that satisfies all of these axioms will be called a legal arrangment. General guidelines for the following questions • The following questions are a mixture of multiple choice and multiple selection questions. • In the multiple choice questions the possible answers are preceded by circular buttons. You must chose exactly one option from those avalable. • In the multiple selection quetions the possible answers are preceded by square tick boxes. You must chose all correct options. The correct answer could be any selection (including none or all) from the option. What is the minimum number of toys allowed in a legal arrangement? 00 01 O 2 O 3 O 4 O 5