2. Which of these are propositions? What are the truth values of those that are propositions?
a) Do not pass go.
This is not a proposition; it 's a command.
b) What time is it?
This is not a proposition; it 's a question.
c) There are no black flies in Maine.
This is a proposition that is false.
d) 4 + x = 5.
This is not a proposition; its truth value depends on the value of x.
e) The moon is made of green cheese.
This is a proposition that is false.
f) 2^n ≥ 100.
This is not a proposition; its truth value depends on the value of n.
4. Let p and q be the propositions p : I bought a lottery ticket this week. q : I won the million dollar jackpot on Friday.
Expression each of these propositions as an English sentence.
a) ¬P
I have not bought a lottery
…show more content…
(p q) → r
f) You will get an A in this class if and only if you either do every exercise in this book or you get an A on the final. r ↔ (p v q)
18. Write each of these statements in the form "if p, then q" in English. [Hint: Refer to the list of common ways to express conditional statements provided in this section.]
a) It is necessary to wash the boss 's car to get promoted.
If you get promoted, then you have washed the boss’s car.
b) Winds from the south imply a spring thaw.
If the winds are from the south, then there will be a spring thaw.
c) A sufficient condition for the warranty to be good is that you bought the computer less than a year ago.
If you bought the computer less than a year ago, then the warranty is good.
d) Willy gets caught whenever he cheats.
If Willy cheats, then he gets caught.
e) You can access the website only if you pay a subscription fee.
If you can access the website, then you must have paid a subscription fee.
f) Getting elected follows from knowing the right people.
If you know the right people, then you get elected.
g) Carol gets seasick whenever she is on a