The compound statement "I do not pass the course if and only if I do not complete my homework" can be written symbolically as follows:

Let:

• $p$: "I pass the course"
• $q$: "I complete my homework"

The negations of these statements are:

• $\neg p$: "I do not pass the course"
• $\neg q$: "I do not complete my homework"

The phrase "if and only if" corresponds to a biconditional statement. Hence, the compound statement becomes:

$\neg p \leftrightarrow \neg q$

This is the symbolic form of the statement.

Would you like further details on biconditional logic or any related concepts? Here are 5 questions to deepen your understanding:

1. What does the biconditional operator $\leftrightarrow$ signify in logic?
2. How would the statement change if it were "I do not pass the course if I do not complete my homework"?
3. Can the biconditional statement $\neg p \leftrightarrow \neg q$ be rephrased using an implication?
4. What truth table represents the biconditional $\neg p \leftrightarrow \neg q$?
5. How would the symbolic form change if the statements $p$ and $q$ were both positive?

Tip: In logic, a biconditional statement $p \leftrightarrow q$ means both statements are either true together or false together!