True or False
Label each of the following statements as either true or false.
The field
Whether the statement, “Every integral domain contains set of positive elements” is true or false.
Answer to Problem 1TFE
Solution:
The statement, “Every integral domain contains set of positive elements” is false.
Explanation of Solution
Formula used:
Definition of ordered integral domain:
If
Explanation:
Consider the statement, “Every integral domain contains set of positive elements.”
By using definition, an element
Thus, every integral domain may or may not contain the set of positive elements.
Hence, the statement “Every integral domain contains set of positive elements” is false.
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Chapter 5 Solutions
Elements Of Modern Algebra
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- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,