Lecture_20 - Lecture 20 Lecture 20 Examples Examples Fix a...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 20 Lecture 20 Examples Examples Fix a language over the following signature: P(­),Q(­),R(­,­),a,b Let M be the following interpretation: X = {0,1,2,3,4} PM = {0,1} QM = {1,3,4} RM = {(0,0),(0,1),(2,1),(2,4),(3,4),(4,0),(4,2)} aM = 1, bM = 3 Evaluate Evaluate ∃ x(¬(x≈ a)∧ P(x)) ∧∃ x(¬(x≈ a)∧ Q(x)) ∃ x(¬(x≈ a)∧ ∧ P(x) Q(x)) ∀x(R(x,x) → R(x,a)) ∀x(R(b,x) → ¬Q(x)) ∃ x∀y(R(x,y) → P(y)) ∀x∃ y(R(x,y) ∧ Q(y)) Find the set Find the set R(x,a) ∃ yR(x,y) ∃ z[R(x,z)∧ R(y,z)] ∀y[R(x,y) →(y ≈ a)] ∀y[R(x,y) →Q(y)] ∃ z[R(x,z)∧ Q(z)] ∧ ≈ y y Find a defining condition Find a defining condition {2,3,4} {0} {0,2,3,4} {1} {(4,2),(2,4),(1,3)} {(0,0,0),(1,1,1),(2,2,2),(3,3,3),(4,4,4)} Give counterexamples to the Give counterexamples to the following ∀x(P(x) ∨ Q(x)) ╞ ∀xP(x) ∨ xQ(x) ∀ ∃ xP(x) ∧∃ xQ(x) ╞ ∃ x(P(x) ∧ Q(x)) ∀x∃ yR(x,y) ╞ ∃ x∀yR(x,y) ∃ x∀yR(x,y) ╞ ∀x∃ yR(x,y) ...
View Full Document

This note was uploaded on 02/27/2011 for the course PHILOSOPHY 101 taught by Professor H during the Spring '11 term at Columbia College.

Ask a homework question - tutors are online