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1. Let H(x) be the statement "x is happy." where the domain is the set of dogs. A. How would you write the statement "all dogs are happy" in the symbols of predicate logic? B. The negation of a statement is its logical opposite; it is true when the statement is false, and false when the statement is true. Write the negation of the statement "all dogs are happy" in English, and also in symbols.

1. Let H(x) be the statement "x is happy." where the domain is the set of dogs. A. How would you write the statement "all dogs are happy" in the symbols of predicate logic? B. The negation of a statement is its logical opposite; it is true when the statement is false, and false when the statement is true. Write the negation of the statement "all dogs are happy" in English, and also in symbols.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Activity 1.3.2: Negating Quantified Statements 1. Let H(x) be the statement "x is happy." where the domain is the set of dogs. A. How would you write the statement "all dogs are happy" in the symbols of predicate logic? B. The negation of a statement is its logical opposite; it is true when the statement is false, and false when the statement is true. Write the negation of the statement "all dogs are happy" in English, and also in symbols. 2. Let X be the set of real numbers in the interval 0 < x s 1. Consider the following statement: For every number x in X, there is a number y in X such that y < x. A. Decide whether this statement is true or false. B. Write the negation of this statement in English. C. Write the above statement, and its negation, in the symbols of predicate logic. 3. Based on your work above, state some symbolic rules you can use to negate a quantified statement. Activity 1.4.2: Models for Axiomatic Systems Undefined terms: zork, gork, snork Axioms: 1. For every pair of zorks z1 and z2 , there is exactly one gork g such that z1 snorks g and z2 snorks g. 2. For every pair of gorks g1 and g2, there is a zork z that snorks both g1 and g2. 3. There are at least four distinct zorks, no three of which snork the same gork. Activities: 1. Fill in the blanks: Let g1 and g2 be a given pair of gorks. By Axiom, some zork z snorks both of them. Suppose another zork z' also snorks both g1 and g2. Then and are each snorked by both and , contradicting Axiom . So there can't be such a zork z, and therefore there is only one zork that snorks both gorks. 2. Draw a model for this system in which a zork is a point, a gork is a line, and "snorks" means "lies on." Use as few zorks as possible. 3. In your model, are there three gorks that are snorked by the same zork? Must this always be the case?
Transcribed Image Text:Activity 1.3.2: Negating Quantified Statements 1. Let H(x) be the statement "x is happy." where the domain is the set of dogs. A. How would you write the statement "all dogs are happy" in the symbols of predicate logic? B. The negation of a statement is its logical opposite; it is true when the statement is false, and false when the statement is true. Write the negation of the statement "all dogs are happy" in English, and also in symbols. 2. Let X be the set of real numbers in the interval 0 < x s 1. Consider the following statement: For every number x in X, there is a number y in X such that y < x. A. Decide whether this statement is true or false. B. Write the negation of this statement in English. C. Write the above statement, and its negation, in the symbols of predicate logic. 3. Based on your work above, state some symbolic rules you can use to negate a quantified statement. Activity 1.4.2: Models for Axiomatic Systems Undefined terms: zork, gork, snork Axioms: 1. For every pair of zorks z1 and z2 , there is exactly one gork g such that z1 snorks g and z2 snorks g. 2. For every pair of gorks g1 and g2, there is a zork z that snorks both g1 and g2. 3. There are at least four distinct zorks, no three of which snork the same gork. Activities: 1. Fill in the blanks: Let g1 and g2 be a given pair of gorks. By Axiom, some zork z snorks both of them. Suppose another zork z' also snorks both g1 and g2. Then and are each snorked by both and , contradicting Axiom . So there can't be such a zork z, and therefore there is only one zork that snorks both gorks. 2. Draw a model for this system in which a zork is a point, a gork is a line, and "snorks" means "lies on." Use as few zorks as possible. 3. In your model, are there three gorks that are snorked by the same zork? Must this always be the case?
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