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)(V)(x,x) (x)(3)(y,x) (3x)(3y)P(y,x) X (b) Negate your expression from part (a), and simplify it so that no quantifier or connective lies within the scope of a neg. (3x)(3)(~P(y, x)) (((()) (3))(-P(x, y)) ((((, x)) (x)(3)(~P(x, x)) X (c) Translate your expression from part (b) into understandable English. Don't use variables in your English translation. 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. There is a number that all numbers are less than or equal to. O All numbers are less than or equal to all numbers.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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asnwer a and b only.

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.
(vx)(3)P(x, y)
(x)(V)(x,x)
(3x)(v)P(x,x)
(V)(3)(x,x)
(3x)(3y)P(y,x)
X
(b) Negate your expression from part (a), and simplify it so that no quantifier or connective lies within the scope of a negation.
(3x)(3)(-P(y, x))
((((, x))
(3x)(V)(-P(x, y))
(3x)(V)(Py, x))
(vx)(3)(~P(y, x))
X
(c) Translate your expression from part (b) into understandable English. Don't use variables in your English translation.
O All numbers have a number that they are less than or equal to.
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.
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. (vx)(3)P(x, y) (x)(V)(x,x) (3x)(v)P(x,x) (V)(3)(x,x) (3x)(3y)P(y,x) X (b) Negate your expression from part (a), and simplify it so that no quantifier or connective lies within the scope of a negation. (3x)(3)(-P(y, x)) ((((, x)) (3x)(V)(-P(x, y)) (3x)(V)(Py, x)) (vx)(3)(~P(y, x)) X (c) Translate your expression from part (b) into understandable English. Don't use variables in your English translation. O All numbers have a number that they are less than or equal to. 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. 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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