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The question in the image asks to translate the statement "I am not going out for dinner if and only if I am feeling tired" into symbolic form, using the given propositions:

- \( p \): Today is Thursday
- \( q \): It is cold outside
- \( r \): I am feeling tired
- \( s \): I am not going out for dinner

The phrase "if and only if" corresponds to the biconditional logical operator \( \leftrightarrow \). 

Thus, the symbolic form for "I am not going out for dinner if and only if I am feeling tired" would be:

\[
\neg s \leftrightarrow r
\]

This matches option **c** in the image: \( \neg s \leftrightarrow r \).

Would you like further details or have any other questions?

Here are some related questions:
1. How do biconditional statements work in logic?
2. What is the difference between "if" and "if and only if"?
3. How do you negate a logical proposition?
4. Can a biconditional statement be false if both parts are true?
5. How would the symbolic form change if "I am not feeling tired"?

**Tip:** The biconditional (↔) statement is true when both statements have the same truth value (either both true or both false).

Translate the statement 'I am not going out for dinner if and only if I am feeling tired' into symbolic form using the propositions: p: Today is Thursday, q: It is cold outside, r: I am feeling tired, s: I am not going out for dinner.

Learn how to translate statements into symbolic form using biconditional logic operators. This example shows how to represent the sentence 'I am not going out for dinner if and only if I am feeling tired' in symbolic form using logical propositions. Suitable for Grades 9-12 students.

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