Questions: Let p and q represent the following simple statements p: The campus is closed. q: It is Sunday Write the following compound statement in symbolic form. The campus is closed if and only if it is Sunday. The compound statement written in symbolic form is p ↔ q

Solution Steps

To convert the given compound statement into symbolic form, we need to understand the logical connectors used. The phrase "if and only if" corresponds to the biconditional logical operator, which is denoted by \( \leftrightarrow \) in symbolic logic. Therefore, the statement "The campus is closed if and only if it is Sunday" can be translated into symbolic form using the given simple statements \( p \) and \( q \).

1. Identify the simple statements and their corresponding symbols:
   • \( p \): The campus is closed.
   • \( q \): It is Sunday.
2. Recognize the logical connector "if and only if" which corresponds to the biconditional operator \( \leftrightarrow \).
3. Combine the simple statements using the biconditional operator to form the compound statement.

We are given two simple statements:

• \( p \): The campus is closed.
• \( q \): It is Sunday.

The phrase "if and only if" corresponds to the biconditional logical operator, which is denoted by \( \leftrightarrow \) in symbolic logic.

Using the biconditional operator, we combine the simple statements \( p \) and \( q \) to form the compound statement: \[ p \leftrightarrow q \]

Final Answer