Introduction
Let r = "It is cold", and s = "It is sunny"| Sentence | Symbolic Form |
|---|---|
| It is not cold. | ~r |
| It is cold and sunny. | r ∧ s |
| It is cold or sunny. | r ∨ s |
| It is not cold but sunny. | ~r ∧ s |
| It is neither cold nor sunny. | ~r ∧ ~s |
Exercises and Solutions
Exercise 1:
Let p, q and r be the following propositions:- p = "you get an A on the final exam"
- q = "you do every exercise in this textbook"
- r = "you get an A in this class"
Question: Write the following propositions using p, q, and r and logical connectives.
- To get an A in this class it is necessary for you to get an A on the final exam. Solution: p → r
- You do exery in this textbook; You get an A on the final exam, implies, you get an A in this class. Solution: q ∧ p → r
- Getting an A on the final exam and doing every evercise in this textbook is sufficient for getting an A in this class. Solution: p ∧ q → r
Exercise 2:
Let p, q and r be the following propositions:- p = "you have the flu"
- q = "you miss the final exam"
- r = "you pass the course"
Question: Express the following propositions as an English sentence.
- p → q. Solution: If you have flu, then you will miss the final exam.
- ~q → r. Solution: If you don't miss the final exam, you will pass the course.
- ~p ∧ ~q → r. Solution: If you neither have flu nor miss the final exam, then you will pass the course.