## Problem 1005

The statement listed below is false. Let p represent the statement.

p: The adult human skull contain of two bones.

Express the symbolic statement   ̴p in words. What can be concluded about the resulting verbal statement?

Solution:-

The symbol   ̴ is translated as “not.” Therefore,    ̴p represents the negation of the given statement, p.

The negation of a statement is statement that has a meaning that is opposite that of the original meaning.

So , in words, the symbolic statement    ̴p is

The adult human skull does not consist of two bones.

The resulting verbal statement is the negation of the initial verbal statement.

Thus, the resulting verbal statement is true because the initial verbal statement is false.

## Problem 1004

Form the negation of the statement.

November does not come before December.

Solution:-

The negative of a statement has a meaning that is opposite that original meaning. The most common way to negate a statement is to introduce not into the sentence.

If a statement is true, then the negation of the statement is a false statement.  Likewise, if a statement is false, the negation of the statement is a true statement.

The following statement negates the original statement by introducing not into the sentence.

It is not true that November does not come before December.

Simplify the English sentence by removing any double negative. Thus, we obtain the negation of the statement “November does not come before December.”

November does come before December.

## Problem 1003

Spiders have six legs.

Is the given sentence a statement?

Solution:-

A statement is a sentence that is either true or false, but not both simultaneously.

Some sentence, such as commands, questions, and opinions, are not statements because they cannot be labeled as true or false.

The given sentence can be labeled as true or false. Actually, the sentence is false.

Therefore, the given sentence is a statement.