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.