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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337280426

Chapter A, Problem 29E

Textbook Problem

Assume that it is true that “Polly sings well,” it is false that “Quentin writes well,” and it is true that “Rita is good at math.” Determine the truth of each of the statements in Exercises 25–32.

Either Polly sings well and Quentin writes poorly, or Rita is good at math.

Expert Solution

To determine

The truth of the statement “Either Polly sings well and Quentin writes poorly, or Rita is good at math.” where it is assumed that the statement “Poly sings well” is true and *“* Quentin writes well *”* is false, and “Rita is good at math” is true.

A sentence is a statement if it is defined as a declarative sentence and whose value is either true or false which is called its truth value.

If *p* is a statement, then the negation of the statement is defined as *p.*

To represent the new statement from old ones, the conjunction is used such as *p* and *q.*

The truth value of this is true if both *p* and *q* are true otherwise, false and Disjunction is used such as *p* or *q.* The truth value of this is true if either *p* or *q* is true or both true.

Consider the statement, *p:* Polly sings well,

The truth value of *p* is true.

Consider the statement, *q*: Quentin writes well,

The truth value of *q* is false.

The statement Quentin writes poorly is represented by the negation of *q,*

The truth value

Finite Mathematics

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