Let p and q represent the following simple statements.

​p:

Upper I pass the course

.

​q:

Upper I complete my homework

.

Write the following compound statement in symbolic form.

Upper I do not pass the course

if and only if

Upper I do not complete my homework

.

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Part 1

The compound statement written in symbolic form is

enter your response here

.

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!

Let p and q represent the following simple statements. p: I pass the course. q: I complete my homework. Write the following compound statement in symbolic form: I do not pass the course if and only if I do not complete my homework.

Learn how to express the statement 'I do not pass the course if and only if I do not complete my homework' in symbolic logic form. This problem covers key logical concepts like biconditional statements and negation, making it suitable for students in Grades 9-12.

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