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The domain for this problem is some unspecified collection of numbers. Consider the predicate P(x, y) = "x is greater than y." (a) Translate the following statement into predicate logic. Every number has a number that is greater than it. (x)(3)(x, y) (((x) (3x)(y)P(x,x) (x)(³)(x,x) O (3x) (³y)P(y,x) (b) Negate your expression from part (a), and simplify it so that no quantifier or connective lies within the scope of a negation. O (3x)(3)(-P(y, x)) ((((, x)) 000000000100

The domain for this problem is some unspecified collection of numbers. Consider the predicate P(x, y) = "x is greater than y." (a) Translate the following statement into predicate logic. Every number has a number that is greater than it. (x)(3)(x, y) (((x) (3x)(y)P(x,x) (x)(³)(x,x) O (3x) (³y)P(y,x) (b) Negate your expression from part (a), and simplify it so that no quantifier or connective lies within the scope of a negation. O (3x)(3)(-P(y, x)) ((((, x)) 000000000100

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 80E
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The domain for this problem is some unspecified collection of numbers. Consider the predicate P(x, y) = "x is greater than y." (a) Translate the following statement into predicate logic. Every number has a number that is greater than it. (x)(3)(x, y) (x), x) (3x)(y), x) (x)(³)(y,x) Ⓒ (3x)(³y)P(y,x) (b) Negate your expression from part (a), and simplify it so that no quantifier or connective lies within the scope of a negation. O (3x)(3)(~P(y, x)) ((((, x)) (3x)(V)(P(x, y)) (3x)(V)(Py, x)) (x)(3)(Py, x)) (c) Translate your expression from part (b) into understandable English. Don't use variables in your English translatio O All numbers have a number that they are less than or equal to. O There is a number that has a number that it is less than or equal to. O There is a number that all numbers are greater than or equal to. O There is a number that all numbers are less than or equal to. O All numbers are less than or equal to all numbers.
Transcribed Image Text:The domain for this problem is some unspecified collection of numbers. Consider the predicate P(x, y) = "x is greater than y." (a) Translate the following statement into predicate logic. Every number has a number that is greater than it. (x)(3)(x, y) (x), x) (3x)(y), x) (x)(³)(y,x) Ⓒ (3x)(³y)P(y,x) (b) Negate your expression from part (a), and simplify it so that no quantifier or connective lies within the scope of a negation. O (3x)(3)(~P(y, x)) ((((, x)) (3x)(V)(P(x, y)) (3x)(V)(Py, x)) (x)(3)(Py, x)) (c) Translate your expression from part (b) into understandable English. Don't use variables in your English translatio O All numbers have a number that they are less than or equal to. O There is a number that has a number that it is less than or equal to. O There is a number that all numbers are greater than or equal to. O There is a number that all numbers are less than or equal to. O All numbers are less than or equal to all numbers.
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