Answer to Question #145831 in Discrete Mathematics for Samantha

Question

Write each statement in symbolic form, using the given symbols.

Let p: I will study
Let q: I will pass the test
Let r: I am foolish

1. I will study or i am foolish
2. I will study or i will not pass the test.
3. I will study and I will pass the test
4. I will past the test or I am foolish
5. I am not foolish and I will pass the test.
6. I will not study or I am foolish
7. I will study or I will not study
8. I will study and I will pass the test or I am foolish.
9. It is not true that i will not study or I am foolish
10. It is not the case that I will not study or I am not foolish

Answer 1

p = I will study

q = I will pass the test

r = I am foolish 

1. I will study or i am foolish: $p \vee r$

2. I will study or i will not pass the test: $p \vee \neg q$

3. I will study and I will pass the test: $p \wedge q$

4. I will past the test or I am foolish: $q \vee r$

5. I am not foolish and I will pass the test: $\neg r \wedge q$

6. I will not study or I am foolish: $\neg p \vee r$

7. I will study or I will not study: $p \vee \neg p$

8. I will study and I will pass the test or I am foolish: $(p \wedge q) \vee r$

9. It is not true that i will not study or I am foolish: $\neg (\neg p \vee r)$

10. It is not the case that I will not study or I am not foolish: $\neg (\neg p \vee \neg r)$