You & maths

The Foundations: Logic and Proofs – Exercises from 1 to 5

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

a) Boston is the capital of Massachusetts.

b) Miami is the capital of Florida.

c) 2 + 3 = 5.

d) 5 + 7 = 10.

e) x + 2 = 11.

f) Answer this question.

Answer:

a) Proposition, T

b) Proposition, T

c) Proposition, T

d) Proposition, F

e) Not a proposition.

f) Not a proposition.

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

a) Do not pass go.

b) What time is it?

c) There are no black flies in Maine.

d) 4 + x = 5.

e) The moon is made of green cheese.

f) 2n ≥ 100.

Answer:

a) not a proposition

b) not a proposition

c) proposition, false

d) not a proposition

e) proposition, false

f) not a proposition

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

a) Linda is younger than Sanjay.

b) Mei makes more money than Isabella.

c) Moshe is taller than Monica.

d) Abby is richer than Ricardo.

Answer:

a) Linda is not younger than Sanjay.

b) Mei does not make more money than Isabella.

c) Moshe is not taller than Monica.

d) Abby is not richer than Ricardo.

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

a) Janice has more Facebook friends than Juan.

b) Quincy is smarter than Venkat.

c) Zelda drives more miles to school than Paola.

d) Briana sleeps longer than Gloria.

Answer:

a) Janice has less Facebook Friends than Juan

b) Quincy isn’t smarter than Venkat

c) Zelda drives less miles to school than Paola

d) Briana doesn’t sleep longer than Gloma

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

a) Mei has an MP3 player.

b) There is no pollution in New Jersey.

c) 2 + 1 = 3.

d) The summer in Maine is hot and sunny.

Answer:

a) Mei does not haw au MP3 player.

b) There is pollution in New Jersey.

c) \large {\color {Blue} 1+2 \neq 3}

d) The summer in Maine is not (hot and sunny).