Translation from English to Symbols
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.
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Date of last modification: February 27, 2019