Questions: Logic Identifying simple and compound statements For each statement, choose if it is simple or compound. If it is compound, choose which type. Statement Type of statement (a) The menu has burritos and tacos. - Simple - Compound - undefined (b) I will get 100% on the test if and only if I get all the answers correct. - Simple - compound (c) Frank is quiet if the movie is playing. - undefined

Logic
Identifying simple and compound statements

For each statement, choose if it is simple or compound. If it is compound, choose which type.

Statement Type of statement

(a) The menu has burritos and tacos.

- Simple
- Compound
- undefined

(b) I will get 100% on the test if and only if I get all the answers correct.

- Simple
- compound

(c) Frank is quiet if the movie is playing.

- undefined

Transcript text: Logic Identifying simple and compound statements For each statement, choose if it is simple or compound. If it is compound, choose which type. \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Statement } & Type of statement \\ \hline (a) The menu has burritos and tacos. & \begin{tabular}{l} Simple \\ Compound \\ undefined \end{tabular} \\ \hline (b) I will get $100 \%$ on the test if and only if I get all the answers correct. & \begin{tabular}{l} Simple \\ compound \end{tabular} \\ \hline (c) Frank is quiet if the movie is playing. & \begin{tabular}{l} undefined \end{tabular} \\ \hline \end{tabular}

Solution

Solution Steps

To determine whether each statement is simple or compound, we need to analyze the logical structure of each statement. A simple statement contains a single idea, while a compound statement contains multiple ideas connected by logical connectors such as "and," "or," "if...then," or "if and only if."

Solution Approach

For statement (a), check if it contains multiple ideas connected by a logical connector.
For statement (b), check if it contains multiple ideas connected by a logical connector.
For statement (c), check if it contains multiple ideas connected by a logical connector.

Step 1: Analyze Statement (a)

The statement "The menu has burritos and tacos." contains the logical connector "and," indicating that it presents multiple ideas. Therefore, it is classified as a compound statement.

Step 2: Analyze Statement (b)

The statement "I will get 100% on the test if and only if I get all the answers correct." contains the logical connector "if and only if," which also indicates multiple ideas. Thus, this statement is classified as a compound statement.

Step 3: Analyze Statement (c)

The statement "Frank is quiet if the movie is playing." contains the logical connector "if," suggesting it presents multiple ideas. Hence, this statement is also classified as a compound statement.