Chapter 3 Review

Form the negation of the statement.

It is 32 $\degree$  outside.

• Sometimes it is not 32 $\degree$  ouside.

• It is not 32 $\degree$  outside.

• It is never 32 $\degree$  outside.

• It is hot outside.

Form the negation of the statement.

Wednesday does not come before Thursday.

• It is not true that Wednesday comes before Thursday.

• Thursday does come before Wednesday.

• Sometimes Wednesday does not come before Thursday.

• Wednesday comes before Thursday.

Let p represent the following statement.

p: One swims fast.

Express the statement One does not swim fast symbolically.

• $\sim$ p

• p

• q

• $\sim$ q

Let p and q represent the following statements:

p: The fire is not burning.

q: There are not nine notes in a major scale.

Express the following statement symbolically.

The fire is burning.

• $\sim q$

• q

• $\sim p$

• p

a. Express the quantified statement in an equivalent way.

All people are temperamental.

• At least one person is temperamental.

• All people are not temperamental.

• Not all people are temperamental.

• There are no people that are not temperamental.

5b. Write the negation of the quantified statement. ( It should begin with "all", "some" or "none.)

All people are temperamental.

• All people are not temperamental.

• No people are temperamental.

• Some people are temperamental.

• Some people are not temperamental.

6 a. Express the quantified statement in an equivalent way.

Some computers are smart.

• No computers are not smart.

• At least one computer is smart.

• There are no computers that are not smart.

• Not all computers are smart.

6 b. Write the negation. ( possible answers)

Some computers are smart.

• Some computers are not smart.

• No computers are not smart.

• All computers are not smart.

• No computers are smart.

What is a statement? Explain why commands, questions, and opinions are not statements.

• A statement is a sentence that is factually false. Commands, questions, and opinions do not meet this criteria.

• A statement is a sentence that is simultaneously true and false. Commands, questions, and opinions do not meet this criteria.

• A statement is a sentence that is factually true. Commands questions and opinions are not.

• A statement is a sentence that is either true or false, but not both simultaneously. commands, questions, and opinions do not meet this.

Let p and q represent the following simple statements:

p: The job pays well.

q: This is an octopus.

Write a compound statement in symbolic form.

The job pays well and this is an octopus.

• $p\ \wedge\ q$

• $p\ \vee\ q$