A blue node An edge connecting a blue node and a green node. [Image source: https://en.wikipedia.org/wiki/Graph_coloring] A simple graph can be expressed by the following two predicates. Given the predicates below: Edge(x, y): x is connected to y Color(x, z): x has color z and the following domains: domain of x and y: {all nodes in a graph}, domain of z: {RED, GREEN, BLUE, YELLOW}, translate the following statements into English. a) Vx 3y Edge(x, y) b) Vz 3x Color(x, z) c) VxVvVz (Edge(x, v)A Color(x. z) → -Color(y, z))

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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A graph (also known as a network) consists of nodes and edges. Edges connect nodes. Graphs/networks
have many real-life applications. One of the most common examples is a social network (e.g., Facebook),
where the people are represented by nodes and friendship/connection between two people is
represented by an edge. See a picture of a graph below where the nodes are colored in red, green, and
blue.
-A blue node
An edge connecting a blue node and a green node.
[Image source: https://en.wikipedia.org/wiki/Graph_coloring]
A simple graph can be expressed by the following two predicates. Given the
predicates below:
Edge(x, y): x is connected to y
Color(x, z): x has color z
and the following domains:
domain of x and y: {all nodes in a graph},
domain of z: {RED, GREEN, BLUE, YELLOW},
translate the following statements into English.
a) Vx3y Edge(x, y)
b) Vz 3x Color(x, z)
c) VxVyVz (Edge(x, y) A Color(x, z) → ¬Color(y, z))
Transcribed Image Text:A graph (also known as a network) consists of nodes and edges. Edges connect nodes. Graphs/networks have many real-life applications. One of the most common examples is a social network (e.g., Facebook), where the people are represented by nodes and friendship/connection between two people is represented by an edge. See a picture of a graph below where the nodes are colored in red, green, and blue. -A blue node An edge connecting a blue node and a green node. [Image source: https://en.wikipedia.org/wiki/Graph_coloring] A simple graph can be expressed by the following two predicates. Given the predicates below: Edge(x, y): x is connected to y Color(x, z): x has color z and the following domains: domain of x and y: {all nodes in a graph}, domain of z: {RED, GREEN, BLUE, YELLOW}, translate the following statements into English. a) Vx3y Edge(x, y) b) Vz 3x Color(x, z) c) VxVyVz (Edge(x, y) A Color(x, z) → ¬Color(y, z))
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