Use quantifiers and predicates with more than one variable

Chapter 7, Problem 14E

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QUESTION:

Problem 14E

Use quantifiers and predicates with more than one variable to express these statements.

a)  There is a student in this class who can speak Hindi.

b)Every student in this class plays some sport.

c) Some student in this class has visited Alaska but has not visited Hawaii.

d)All students in this class have learned at least one programming language.

e)  There is a student in this class who has taken every course offered by one of the departments in this school.

f) Some student in this class grew up in the same town as exactly one other student in this class.

g) Every student in this class has chatted with at least one other student in at least one chat group.

Questions & Answers

QUESTION:

Problem 14E

Use quantifiers and predicates with more than one variable to express these statements.

a)  There is a student in this class who can speak Hindi.

b)Every student in this class plays some sport.

c) Some student in this class has visited Alaska but has not visited Hawaii.

d)All students in this class have learned at least one programming language.

e)  There is a student in this class who has taken every course offered by one of the departments in this school.

f) Some student in this class grew up in the same town as exactly one other student in this class.

g) Every student in this class has chatted with at least one other student in at least one chat group.

ANSWER:

Solution :

Step 1:

In this problem we have to express  the given statements using quantifiers.

We know that the quantifiers:

Negation “NOT”  :

Conjunction “AND” : “

Disjunction “” :  “

If then “implies” : “

If and only if : “

For all “every one” :

There Exists “any one” : “

The existential quantifiers of the negation is :

This is logically equivalent to :

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