Axiomatisation of the Vegetables and Toys Competition All entries to this competition must strictly obey all formulae in a set of traditional axioms, otherwise they will be disqualified. The axioms...

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Extracted text: Axiomatisation of the Vegetables and Toys Competition All 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 following specification (key): Domain of discourse: All items on the tea tray V(2) Item a is a vegetable T(z) Item z is a toy B(x, y) Item a is balanced on item y. Notes: • The possible numbers of entities in the domain is not specified explicitly, but may be restricted 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 items on the tray, not the tray. It is required that a single tea tray is used, satisfying British tea tray regulations and appropriate standards of taste and decency. It should preferably be a family heirloom. • The category of vegetable also includes so-called "fruit" -- tomatoes and cucumbers are welcome, and of course rhubarb. For the real competition, the fruit must have been grown by the 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 awarded for arrangements involving knitted toys made by the contestant, but this is not a strict requirement. Rule Axiom Rule Name 1. Vz[V(x)V T(x)) Essential Ontological Precondition 2. B3y3z[V(x) ^ V (y) A-(2 = y) A T(z)] Rule of Plenty VæVyVzvw[ (V(x) A V(y) A V (2) A V(w)) + (x = y Vr = z Va = w V y = z V y = w V z = w) ] 3. Yorkshire Rule of Parsimony 4. -3æ(V (z) A T(x)] Requirement of Good Taste


Extracted text: 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 own Λ Β(π, υ) Λ (ψ, υ] 7. -3a3y[B(x,y) ^ B(y, x)] Balancing Principle 1 8. Vævyvz[(B(x, y) ^ B(y, z)) → ¬B(x, z)] Balancing Principle 2 9. -3Jy3z3w[B(x, y) ^ B(y, z) A B(z,w)] Health and Safety 10. -3a3yaz(¬(y = z) A B(x, y) A B(x, z)] The 'no straddling' rule - peculiar to Otley 11. Jarvy[ Vz[¬B(y, z)] + (y = x) ] 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? 01 O 2 O 3 4 O 5