1

I was working through these questions and I just wanted to verify my answers since I don't have access to any solutions and I wanted to make sure I was on the right track:

Let the following be the non-logical symbols of CQL (classical quantificational logic): IS = {a, b, c}, VR (variables) = {x,y,z}, RS1 (one-place predicates) = {F,G,H} and RS2 (two-place predicates) = {R,S,T}.

  1. Determine the truth-value of the formulae listed below, in light of the following model: M = ⟨U, i⟩, where U (universe of discourse) = {1, 2} and i: a􏰀→1; b 􏰀→ 2; S 􏰀→ ∅; R 􏰀→ {⟨1, 1⟩, ⟨2, 2⟩}

(a) ∀x∀y(Sxy → Rxy); Proposed Answer: True since nothing satisfies S so the antecedent is always False.

(b) ∀x∀y((Rxy ∧ Sxy) → Syx); Proposed Answer: True (same reasoning as a)

(c) ∀x∀y((Rxy ∧ ¬Sxy) → Ryx); Proposed Answer: True

(d) ∀x∀y((Rxy ∧ Ryx) → ∃z(Rxz ∨ Syz)); Proposed Answer: True

  1. State the truth-value of the formulae listed below, in light of the following model: M = ⟨U, i⟩, where U = Z+10 (that is, the natural numbers 1 through 10) and R and S are interpreted as < and ≤ respectively (that is, Rab is interpreted as a < b and Sab is interpreted as a ≤ b).

(a) ∀xSxx; Answer: True, since every number is equal to itself.

(b) ∀x∀y(Rxy → ¬Ryx); Answer: True

(c) ∀x∀y∀z((Rxy ∧ Ryz) → Rzx); Answer: False

(d) ∃x∀ySyx; Answer: True (the natural number 10 satisfies this formula)

2

These all appear to be correct.

  • 1
    Great! Thank you very much for your feedback! – DiscipleOfKant Dec 3 '17 at 15:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.