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).