Chapter 3, Problem 1RE

In Exercises 1-4, write the negation of the statement.

1. All Acuras are Hondas.

To determine

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”.