# Translation from English to Symbols

Let r = "It is cold", and s = "It is sunny"
SentenceSymbolic 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.
1. To get an A in this class it is necessary for you to get an A on the final exam. Solution: p → r
2. 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
3. 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.
1. p → q. Solution: If you have flu, then you will miss the final exam.
2. ~q → r. Solution: If you don't miss the final exam, you will pass the course.
3. ~p ∧ ~q → r. Solution: If you neither have flu nor miss the final exam, then you will pass the course.
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Date of last modification: February 27, 2019