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Elementary Geometry for College St...

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

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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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Sect-1.1 P-11ESect-1.1 P-12ESect-1.1 P-13ESect-1.1 P-14ESect-1.1 P-15ESect-1.1 P-16ESect-1.1 P-17ESect-1.1 P-18ESect-1.1 P-19ESect-1.1 P-20ESect-1.1 P-21ESect-1.1 P-22ESect-1.1 P-23ESect-1.1 P-24ESect-1.1 P-25ESect-1.1 P-26ESect-1.1 P-27ESect-1.1 P-28ESect-1.1 P-29ESect-1.1 P-30ESect-1.1 P-31ESect-1.1 P-32ESect-1.1 P-33ESect-1.1 P-34ESect-1.1 P-35ESect-1.1 P-36ESect-1.1 P-37ESect-1.1 P-38ESect-1.1 P-39ESect-1.1 P-40ESect-1.1 P-41ESect-1.1 P-42ESect-1.1 P-43ESect-1.1 P-44ESect-1.1 P-45ESect-1.1 P-46ESect-1.1 P-47ESect-1.1 P-48ESect-1.1 P-49ESect-1.1 P-50ESect-1.1 P-51ESect-1.1 P-52ESect-1.1 P-53ESect-1.1 P-54ESect-1.1 P-55ESect-1.1 P-56ESect-1.1 P-57ESect-1.2 P-1ESect-1.2 P-2ESect-1.2 P-3ESect-1.2 P-4ESect-1.2 P-5ESect-1.2 P-6ESect-1.2 P-7ESect-1.2 P-8ESect-1.2 P-9ESect-1.2 P-10ESect-1.2 P-11ESect-1.2 P-12ESect-1.2 P-13ESect-1.2 P-14ESect-1.2 P-15ESect-1.2 P-16ESect-1.2 P-17ESect-1.2 P-18ESect-1.2 P-19ESect-1.2 P-20ESect-1.2 P-21ESect-1.2 P-22ESect-1.2 P-23ESect-1.2 P-24ESect-1.2 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P-12CTSect-1.CT P-13CTSect-1.CT P-14CTSect-1.CT P-15CTSect-1.CT P-16CTSect-1.CT P-17CTSect-1.CT P-18CTSect-1.CT P-19CTSect-1.CT P-20CTSect-1.CT P-21CTSect-1.CT P-22CTSect-1.CT P-23CT

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