The question on your homework asks you to write an English sentence for the logical expression: ¬p → r, where the following statements are defined:

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

The expression ¬p → r translates to:

• ¬p: Today is not Thursday
• →: implies
• r: I am feeling tired

So, the sentence would be: "If today is not Thursday, then I am feeling tired."

Now let's analyze the answer choices:

a) "Today is not Thursday if and only if I am feeling tired." – This is not correct because it expresses a biconditional (if and only if), which is not the same as ¬p → r.

b) "Today is Thursday and I am feeling tired." – This is also incorrect because it describes a conjunction, which doesn't match the conditional ¬p → r.

c) The remaining option (cut off in the image) seems likely to describe the correct conditional based on the format, but you'll need to confirm that it matches the correct logic: "If today is not Thursday, then I am feeling tired."

Let me know if you want to check the cut-off part or discuss further details!

Here are five questions related to this concept:

1. What is the difference between a conditional statement and a biconditional statement?
2. How would you express ¬p ∧ r in English?
3. Can you describe the logical meaning of p → ¬r?
4. What is the truth table for the expression ¬p → r?
5. How does the negation of a conditional statement, ¬(¬p → r), translate into English?

Tip: In logic, a conditional statement is only false when the first part is true, and the second part is false.