Concept explainers
In Exercises 1-4, write the negation of the statement.
1. All Acuras are Hondas.
To write: The negation of the statement “All Acuras are Hondas”.
Answer to Problem 1RE
The negation of the statement “All Acuras are Hondas” is “Some Acuras are not Hondas”.
Explanation of Solution
Result used:
A statement which gives the exact opposite meaning of the given statement is called its negation
The negation of quantified statements is summarized as follows.
Form of statement | Form of negation |
All are | Some are not |
None are | Some are |
Some are | None are |
Some are not | All are |
Calculation:
The given statement is “All Acuras are Hondas”.
Using the above table from the result, the negation of “All are” is “Some are not”.
That is, “All Acuras are Hondas” can be written as “Some Acuras are not Hondas”.
Therefore, the negation of the given statement is “Some Acuras are not Hondas”.
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Chapter 3 Solutions
A Survey of Mathematics with Applications (10th Edition) - Standalone book
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