a d f g Using the following predicates: square(x) is true if x is a square (otherwise it is false) star (x) is true if x is a star (otherwise it is false) circ(x) is true if x is a circle (otherwise it is false) shade (x) is true if x is shaded (otherwise it is false) next.to(x, y) is true if x and y are adjacent horizontally, vertically or diagonally. This relation is not reflexive for any object. For each of the statements below, determine whether the statement is true or false. You need not justify your response. 3r circ(r) A shade(x) Va shade(r) V ¬shade(r) Vasquare(r) → ¬shade(r) Varvy(star(x) A ¬shade(x) A next.to(x, y) → shade(y) ^ circ(y)) next.to(x, y) ^ shade(r) 3aVy next.to(x, y) A shade(x)
a d f g Using the following predicates: square(x) is true if x is a square (otherwise it is false) star (x) is true if x is a star (otherwise it is false) circ(x) is true if x is a circle (otherwise it is false) shade (x) is true if x is shaded (otherwise it is false) next.to(x, y) is true if x and y are adjacent horizontally, vertically or diagonally. This relation is not reflexive for any object. For each of the statements below, determine whether the statement is true or false. You need not justify your response. 3r circ(r) A shade(x) Va shade(r) V ¬shade(r) Vasquare(r) → ¬shade(r) Varvy(star(x) A ¬shade(x) A next.to(x, y) → shade(y) ^ circ(y)) next.to(x, y) ^ shade(r) 3aVy next.to(x, y) A shade(x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Tarski World
a
g.
Using the following predicates:
square (x) is true if x is a square (otherwise it is false)
star(x) is true if x is a star (otherwise it is false)
circ(x) is true if x is a circle (otherwise it is false)
shade (x) is true if x is shaded (otherwise it is false)
next.to(x, y) is true if x and y are adjacent horizontally, vertically or diagonally. This relation is
not reflexive for any object.
For each of the statements below, determine whether the statement is true or false. You need
not justify your response.
3xcirc(x) A shade(xr)
Va shade(r) V ¬shade(r)
Va square(r) → ¬shade(r)
Vævy(star(r) A ¬shade(r) A next.to(x, y) → shade(y) ^ circ(y))
vr next.to(x, y) A shade(r)
3rvy next.to(r, y) A shade(r)
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