   Chapter 1.1, Problem 57E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercises 55 and 56, P is a true statement, while Q and R are false statements. Classify each of the following statements as true or false.a) P   a n d   Q   o r   ~ R b) P   o r   Q   a n d   ~ R

To determine

a)

To classify:

Each statement as true or false.

Explanation

Approach:

Conjunction:

In logic, a conjunction is a compound sentence formed by using the word and to join two simple sentences.

If P and Q are letters used to represent simple statements, then a statement of the form “P and Q” is known as a conjunction of statement P and statement Q.

The truth of a conjunction is given by:

 P Q P and Q T T T T F F F T F F F F

In the above table, T = True, F = False.

Thus, a conjunction is true only when both P and Q are true.

Disjunction:

In logic, disjunctions are compound sentences made up of two or more simple sentences connected with “or”.

If P and Q are letters used to represent simple statements, then a statement of the form “P or Q” is known as a disjunction of statement P and statement Q.

The truth of a disjunction is given by:

 P Q P and Q T T T T F T F T T F F F

In the above table, T = True, F = False.

Thus, a disjunction is true when either of the statements is true. A disjunction is false only when both the statements are false.

Negation of a statement:

The negation of a given statement P makes a claim opposite that of the original statement. If the given statement is true, its negation is false, and vice versa. If P is a statement, we use ~P (which is read “not P”) to indicate its negation.

Procedure:

The given statement is: P and Q or ~R

The truth value of each statement is as follows:

 Statement Truth Value P T Q F R F

First, let’s evaluate the bracket P and Q

To determine

b)

To classify:

Each statement as true or false.

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