Section 1.2 solutions
THERE IS NOT MUCH WORK SHOWN IN THIS SECTION. I JUST WASN’T SURE WHAT TO WRITE.
PLEASE VISIT ME IF YOU AREN’T UNDERSTANDING THIS SECTION.
Homework #1 – 8. Write a word description of each set
(I’m not sure how to show work for these problems. See me if you need some help.)
1) D = {2, 3, 4, …}
Answer: Natural numbers greater than or equal to 2.
It would be correct to say: Natural numbers greater than 1.
3) A = {1,2,3,4,5,6,7}
Answer: Natural numbers between 1 and 7 inclusive.
5) D = {Bashful, Doc, Dopey, Grumpy, Happy, Sleepy, Sneezy}
Answer: The seven dwarfs.
7) V = {a, e, i, o, u}
Answer: The vowels of the alphabet
Homework #9 – 16: Write the sets in set-builder form. (There are many correct answers.)
(I’m not sure how to show work for these problems. See me if you need some help.)
There are many correct answers.
9) D = {2, 3, 4, …}
Answer 1: D= { x | x is a Natural number and x is greater than or equal to 2 }
Answer 2: D = {{𝑥|𝑥 ∈ 𝑁, 𝑥 ≥ 2} }
11) A = {1,2,3,4,5,6,7}
Answer 1: A = { x | x is a Natural number and 1 ≤ 𝑥 ≤ 7 }
Answer 2: A = {𝑥|𝑥 ∈ 𝑁, 1 ≤ 𝑥 < 8} }
Answer 3: A = { x | x is a Natural number and 𝑥 ≤ 7 }
13) P = set of natural numbers between 3 and 11 inclusive
Answer 1: P = { x | x is a Natural number and 3 ≤ 𝑥 ≤ 11 }
Answer 2: P = {{𝑥|𝑥 ∈ 𝑁, 2 < 𝑥 < 12} }
15) P = set of natural numbers between 3 and 11 exclusive
Answer: P = { x | x is a Natural number and 3 < 𝑥 < 11 }
Homework # 17 – 32. Write sets in roster form.
17) The set of natural numbers between 5 and 10 inclusive.
I need to include the endpoints.
Answer: {5,6,7,8,9,10}
19) The set of even natural numbers greater than 4.
Answer: {4,6,8,…}
21) The set of natural numbers greater than 4.
Answer: {4,5,6…}
23) The set of natural numbers that are negative.
There are no natural numbers that are negative. There are no elements in this set. The answer
needs to be the empty set.
Answer: { }
25) B = { k | k+1=6 }
Solve k + 1 = 6
And get k = 5
Answer: {5}
27) C = { m | m is a natural number, m < 3}
1 and 2 are the only natural numbers less than 3.
Answer: {1,2}
29) D = { m ∈ 𝑁, 2 < m < 5}
This wants Natural numbers between 2 and 5, but I don’t include either the 2 or the 5.
Answer: {3,4}
31) D = { m ∈ 𝑁, 2 < m ≤5}
This wants Natural numbers between 2 and 5, but I don’t include 2, but I do include the 5.
Answer: {3,4,5}