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:

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 33EQ

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