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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!

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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.

Write an English sentence for ¬p → r, where 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 a conditional logic statement like ¬p → r into English. This problem explores logical implications and propositional logic, focusing on negations and conditionals.

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