1. Logic of Informatics
Rule of Inference

2. Rule of Inference

3. Question 1
∼ 𝐴 → (𝐶 ∧ 𝐷)
𝐴 → 𝐵
∼ 𝐵
Prove: 𝐶

4. Question 2
𝑃 ∧ 𝑄
𝑃 →∼ (𝑄 ∧ 𝑅)
𝑆 → 𝑅
Prove: ~𝑆

5. Question 3
~(𝐴∨𝐵)→C ~𝐴 ~𝐶
Prove: 𝐵

6. Question 4 A : I made a B on the test. B : I made an A on the test.
C : I am happy with my test grade.
D : I think I will make a good grade in the course.
Argument:
If I made an B or an A on the test, then I am happy with my test grade.
If I am happy with my test grade, then I think I will make a good grade in the course.
I do not think I will make a good grade in the course.
Therefore I did not make an A on the test.

7. Question 5 P: I drink coffee. Q: I will get a lot of work done.
R: I am sleepy.
S: I am grumpy.
Argument:
If I drink coffee, then I will get a lot of work done.
If I don’t drink coffee, then I am sleepy.
If I am sleepy, then I am grumpy.
Therefore if I don’t get a lot of work done, then I am grumpy.

8. Question 6
Premise #1: If the book is returned within 2 weeks, then there is no fine.
Premise #2: You pay a fine or you may not check out another book.
Premise #3: You are allowed to check out another book.
Conclusion: So, the book was not returned within 2 weeks.

9. Question 7
Premise #1: If this is a good product, then we should buy it.
Premise #2: Either it was made by XYZ Corporation, or we will not buy it.
Premise #3: It is not made by XYZ Corporation.
Conclusion: So, it is not a good product

10. Question 8 Premise #1: If Bill is patient, then he will succeed.
Premise #2: Bill will get bonus pay if he succeeds.
Premise #3: Bill did not get bonus pay.
Conclusion: So, Bill is not patient

11. Question 9
Premise #1: If Sue drives to work, then she will stop at the grocery store.
Premise #2: If she stops at the grocery store, then she’ll buy milk.
Premise #3: Sue drove to work today.
Conclusion: So, Sue will get milk.

12. Question 10 With these hypotheses:
“It is not sunny this afternoon and it is colder than yesterday.”
“We will go shopping only if it is sunny.”
“If we do not go shopping, then we will take a canoe trip.”
“If we take a canoe trip, then we will be home by sunset.”
Using the inference rules, construct a valid argument for the conclusion: “We will be home by sunset.”