Answer to Question #72463 in Discrete Mathematics for BABATUNJI ABDULWAHAB

Question

Answer each question completely, including all lettered parts.

1. Which of these sentences are propositions? What are the
truth values of those that are propositions?

a) Miami is the capital of Florida.
b) 2 + 3 = 5.
c) 5 + 7 = 10.
d) x + 2 = 11.
e) Answer this question.
f) What time is it?


2. What is the negation of each of these propositions?

a) Mei has an MP3 player.
b) There is no pollution in New Jersey.


3. Let p and q be the propositions.


p: I bought a lottery ticket this week.

q: I won the million-dollar jackpot on Friday.


Express of each of these propositions as an English sentence:

a) ~p
b) p^q
c) p v q
d) (~p) ^ (~q)


4. Let p, q, and r be the propositions

p: You have the flu.
q: You miss the final examination.
r: You pass the course.

Express each of these propositions as an English sentence.
a) p → q
b) ~q ↔ r
c) q →~r
d) p ∨ q ∨ r

Answer 1

1. Which of these sentences are propositions? What are the
truth values of those that are propositions?

a) Miami is the capital of Florida. – False.
b) 2 + 3 = 5. – True.
c) 5 + 7 = 10. – False.

2. What is the negation of each of these propositions?

a) Mei has an MP3 player. – Mei does not have an MP3 player.
b) There is no pollution in New Jersey. – There is pollution in New Jersey.

3. Let p and q be the propositions.


p: I bought a lottery ticket this week.

q: I won the million-dollar jackpot on Friday.


Express of each of these propositions as an English sentence:

a) ~p – I didn’t buy a lottery ticket this week.
b) p^q – I bought a lottery ticket this week and I won the million-dollar jackpot on Friday.
c) p v q – I bought a lottery ticket this week or I won the million-dollar jackpot on Friday.
d) (~p) ^ (~q) – I didn’t buy a lottery ticket this week and I didn’t win the million-dollar jackpot on Friday.
 
4. Let p, q, and r be the propositions

p: You have the flu.
q: You miss the final examination.
r: You pass the course.

Express each of these propositions as an English sentence.
a) p → q – If you have the flu, then you will miss the final examination.
b) ~q ↔ r – You will not miss the final examination if and only if you pass the course.
c) q →~r – If you miss the final examination, then you won’t pass the course.
d) p ∨ q ∨ r – You will have the flu or you will miss the final examination or you will pass the course.