Let p and q represent the following simple statements.

​p: 

The office is closedThe office is closed.

​q: 

It is SundayIt is Sunday.

Write the following compound statement in symbolic form.

It is not SundayIt is not Sunday 

if and only if 

the office is not closedthe office is not closed.

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Part 1

The compound statement written in symbolic form is 

enter your response here


The compound statement "It is not Sunday if and only if the office is not closed" can be written in symbolic form as follows:

\[
\neg q \iff \neg p
\]

Where:
- \( p \): The office is closed.
- \( q \): It is Sunday.
- \( \neg q \): It is not Sunday.
- \( \neg p \): The office is not closed.

This uses the biconditional operator (\(\iff\)), representing "if and only if."

Would you like further explanation, or have any questions about this?

### 5 Related Questions:
1. What is the difference between "if and only if" and "if" in logic?
2. How do you negate a compound statement involving "and" and "or"?
3. What are truth tables, and how can they be used to verify compound statements?
4. What is the symbolic form of "The office is closed, and it is Sunday"?
5. How can the contrapositive of a conditional statement be written in symbolic form?

### Tip:
Always remember that "if and only if" (\(\iff\)) means both directions of the implication must be true for the compound statement to hold.

Let p and q represent the following simple statements.

p: The office is closed.
q: It is Sunday.

Write the following compound statement in symbolic form.

It is not Sunday if and only if the office is not closed.

Learn how to express the statement 'It is not Sunday if and only if the office is not closed' in symbolic form using concepts of symbolic logic and biconditional statements. This problem covers key logical concepts such as negation and biconditional connectives, suitable for students in Grades 9-12.

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