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3. Consider the Tarski world shown below: Let Triangle(x), Circle(x), and Square(x) mean “x is a triangle," “x is a circle," and “x is a square"; let Blue(x), Gray(x), and Black(x) mean “x is blue," “x is gray," and “x is black"; let RightOf(x, y), Above(x, y), and SameColorAs(x, y) mean “x is to the right of y," “x is above y," and “x has the same color as y"; and use the notation x = y to denote the predicate “x is equal to y". Let the common domain D of all variables be the set of all the objects in the Tarski world. Each of the following statements is true or false. And explain why. a. For all squares x there is a circle y such that x and y have different colors and y is above x.

3. Consider the Tarski world shown below: Let Triangle(x), Circle(x), and Square(x) mean “x is a triangle," “x is a circle," and “x is a square"; let Blue(x), Gray(x), and Black(x) mean “x is blue," “x is gray," and “x is black"; let RightOf(x, y), Above(x, y), and SameColorAs(x, y) mean “x is to the right of y," “x is above y," and “x has the same color as y"; and use the notation x = y to denote the predicate “x is equal to y". Let the common domain D of all variables be the set of all the objects in the Tarski world. Each of the following statements is true or false. And explain why. a. For all squares x there is a circle y such that x and y have different colors and y is above x.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3. Consider the Tarski world shown below: Let Triangle(x), Circle(x), and Square(x) mean “x is a triangle," “x is a circle," and "x is a square"; let Blue(x), Gray(x), and Black(x) mean “x is blue," "x is gray," and "x is black"; let RightOf(x, y), Above(x, y), and SameColorAs(x, y) mean “x is to the right of y," “x is above y," and "x has the same color as y"; and use the notation x = y to denote the predicate “x is equal to y". Let the common domain D of all variables be the set of all the objects in the Tarski world. Each of the following statements is true or false. And explain why. a. For all squares x there is a circle y such that x and y have different colors and y is above x. b. There is a triangle x such that for all circles y, y is above x.
Transcribed Image Text:3. Consider the Tarski world shown below: Let Triangle(x), Circle(x), and Square(x) mean “x is a triangle," “x is a circle," and "x is a square"; let Blue(x), Gray(x), and Black(x) mean “x is blue," "x is gray," and "x is black"; let RightOf(x, y), Above(x, y), and SameColorAs(x, y) mean “x is to the right of y," “x is above y," and "x has the same color as y"; and use the notation x = y to denote the predicate “x is equal to y". Let the common domain D of all variables be the set of all the objects in the Tarski world. Each of the following statements is true or false. And explain why. a. For all squares x there is a circle y such that x and y have different colors and y is above x. b. There is a triangle x such that for all circles y, y is above x.
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