Concept explainers
a.
To explain:
A logical statement.
Answer to Problem 1PS
Solution:
A logical statement is a declarative sentence that is either true or false, but not both true and false.
Explanation of Solution
Logic is a method of reasoning which accepts only those conclusions that are unable to avoid such that every concept is defined.
If the information is correct, then the statement is true. If not, the statement is false.
That is, a logical statement is a declarative sentence that is either true or false, but not both true and false.
A simple statement is a logical statement which contains one piece of information.
b.
To explain:
A tautology.
Answer to Problem 1PS
Solution:
A tautology is a logical statement which is always true whatever the premises given.
Explanation of Solution
A tautology is logical statement in which the conclusion is equivalent to the premise.
That is, a tautology is a logical statement which is always true whatever the premises given.
c.
To explain:
The law of contraposition.
Answer to Problem 1PS
Solution:
A conditional may always be replaced by its contrapositive without having its truth value affected.
Explanation of Solution
Not all the statements are equivalent in meaning. The converse and inverse statements have the same truth values as the contrapositive and the original statement.
That is,
This required result is called the law of contraposition.
A conditional may always be replaced by its contrapositive without having its truth value affected.
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Chapter 3 Solutions
EBK NATURE OF MATHEMATICS
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,