
Concept explainers
What is a logical statement?

The definition of a logical statement.
Answer to Problem 1FCCE
Solution:
A logical statement is a declarative sentence that is either true or false.
Explanation of Solution
A logical statement is a declarative sentence that is either true or false.
To be a logical statement, the given sentence “The universe is 1 billion years old.” must meet two conditions:
1. It is a declarative sentence.
2. It is TRUE or FALSE.
Declarative Sentence? | TRUE or FALSE | Conclusion |
Yes | It is TRUE or FALSE (not sure of which) | Logical Statement |
Hence, the given sentence “The universe is 1 billion years old.” is a logical statement.
The logical statements can be combined using connectives, words like “and” and “or”.
Implications can be stated with the words “if “and “then”.
The logical statements can be negated with the word “not”.
A logical compound statement is formed by combining the statements by use of the words “and”, “or”, “not”, or “if, then”.
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Chapter 11 Solutions
Finite Mathematics & Its Applications (12th Edition)
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