Consider the following Tarski world (same world as the previous question, but different questions): AO d. e h Predicates exist as follows: Blue(x) means "x is blue" (and similarly for the other two colors) Triangle(x) means "x is a triangle" (and similarly for the other two shapes) RightOf(x.y) means "x is to the right of y" although possibly in a different row. ShapeSame(x.y) means x is the same shape as y" ColorSame(x,y) means "x is the same color as y RowSame(x.y) means "x is in the same row as y For each of the following statements, say whether the statement is T or F, and then say why. When saying why, you may use the letter c to refer to shape c on the Tarski world, and so on. a) 3 x, Vy, Square(x) ^ (Blue(y) v ~ RightOf(x,y)) Tor F: If False, give a value for y for which no such x exists. If True, give a value for x for which the statement is True: b) Vx, Vy, (x*y a RowSame(x,y) →(~ ShapeSame(x,y) ^ ~ColorSame(x,y)) Tor F: If False, give values for x, y for which the statement is false. If True, describe the meaning of the statement in words (one sentence): c) 3w, Vv, (w- v) → RightOf(v, w) Tor F: If True, give a value of w for which it is true; if False, give a value for v for which there is no such w:
Consider the following Tarski world (same world as the previous question, but different questions): AO d. e h Predicates exist as follows: Blue(x) means "x is blue" (and similarly for the other two colors) Triangle(x) means "x is a triangle" (and similarly for the other two shapes) RightOf(x.y) means "x is to the right of y" although possibly in a different row. ShapeSame(x.y) means x is the same shape as y" ColorSame(x,y) means "x is the same color as y RowSame(x.y) means "x is in the same row as y For each of the following statements, say whether the statement is T or F, and then say why. When saying why, you may use the letter c to refer to shape c on the Tarski world, and so on. a) 3 x, Vy, Square(x) ^ (Blue(y) v ~ RightOf(x,y)) Tor F: If False, give a value for y for which no such x exists. If True, give a value for x for which the statement is True: b) Vx, Vy, (x*y a RowSame(x,y) →(~ ShapeSame(x,y) ^ ~ColorSame(x,y)) Tor F: If False, give values for x, y for which the statement is false. If True, describe the meaning of the statement in words (one sentence): c) 3w, Vv, (w- v) → RightOf(v, w) Tor F: If True, give a value of w for which it is true; if False, give a value for v for which there is no such w:
Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Consider the following Tarski world (same world as the previous question, but different questions):
A
b
a
h
j
k
Predicates exist as follows:
Blue(x) means "x is blue" (and similarly for the other two colors)
Triangle(x) means "x is a triangle" (and similarly for the other two shapes)
RightOf(x,y) means "x is to the right of y" although possibly in a different row.
ShapeSame(x,y) means "x is the same shape as y"
ColorSame(x,y) means "x is the same color as y"
RowSame(x,y) means "x is in the same row as y"
For each of the following statements, say whether the statement is T or F, and then say why. When saying why, you may use the letter c to refer to shape c on the Tarski world, and so on.
a) 3 x, Vy, Square(x) ^ (Blue(y) v ~ RightOf(x,y))
Tor F:
If False, give a value for y for which no such x exists. If True, give a value for x for which the statement is True:
b) Vx, Vy, (xy ^ RowSame(x,y)) → (~ Shape Same(x,y) A ~ ColorSame(x,y))
T or F:
If False, give values for x, y for which the statement is false. If True, describe the meaning of the statement in words (one sentence):
c) 3w, Vv, (w # v) → RightOf (v, w)
Tor F:
If True, give a value of w for which it is true; if False, give a value for v for which there is no such w:
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