Answer

Here you go:

If A (subset symbol) B and B(Subset symbol) C, what can you conclude? Why?

A must be a subset of C, since if everything in A is in B, and everything in B is in C, it follows that everything in A is in C.

What if A (proper subset) B and B (proper subset) C?

A is a proper subset of C

If A(subset) B and B (proper subset) C?

A is a subset of C

2. (4 points) Write down all possible subsets of {x, y, z}
The empty set:
{}
One letter:
{x}
{y}
{z}
two letters:
{x,y}
{x,z}
{y,z}
three letters:
{x,y,z}

3. (2 points) Without writing them down, what are the number of subsets of the set A = {a, b, c, d, e}?
2^5 = 32

 

Of set B = {a, b, c, d, e, f, g, h, i}?
2^9 = 512

4. (7 pts) Given U = {All letters of the alphabet}, A = {c, d, e, f}, and B = {e, f, g, h, k}.
List the elements of set

(a) A U B
{c, d, e, f, g, h, k}

(b) A n B
{e, f}

(c) A' n B'
{a, b, i, j, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}

(d) A' U B'
everything but the answer to (b):
{a, b, c, d, g, h, i, j, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}

(e) A U B'
everything but g, h, k:
{a, b, c, d, e, f, i, j, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}

(f) (A U B') n B
same as part b:
{e, f}

(g) (A U B) n (A U B')
{c, d, e, f}

 

5. (2 points) Write the following in roster form:
Set N is the set of natural numbers between two and nine.
Since it's "between", we can assume that 2 and 9 are not included:
J = {3, 4, 5, 6, 7, 8}

 

6. (2 points) State whether set A and B are equal, equivalent, both, or neither.
A = {9, 8, 7} B = {8, 9, 10}
equivalent, since the elements are different but they have the same number of elements

 

7. (2 points) Express the following in set-builder notation: M = {3, 4, 5, 6, 7}
M = {x | x€Z, 3 <= x <= 7}

 

8. (8 pts) A drug company is considering manufacturing a new product that has two different flavors, orange and cherry.
They surveyed 150 people. The results are as follows:

75 liked cherry flavor
94 liked orange flavor
22 liked both flavors.

Construct a Venn diagram and answer the following:

	View Full Image

a) How many liked only orange flavor?
72
b) How many liked only cherry flavor?
54
c) How many liked either one or the other or both?
147
d) How many liked neither?
3

9. (10 pts) In a survey of 75 resorts, it was reported that:

45 provided refrigerators in the guest rooms
37 provided laundry services
44 provided business centers
23 provided refrigerators in the guest rooms and laundry services
29 provided refrigerators in the guest rooms and business centers
21 provided laundry services and business centers
12 provided all three features

Construct a Venn diagram and use it to answer the following questions:

	View Full Image

(a) How many of the resorts provided only refrigerators in the guest rooms?
5
(b) How many of the resorts provided exactly one of the features?
16
(c) How many of the resorts provided at least one of the features?
65
(d) How many of the resorts provided exactly two of the features?
37
(e) How many of the resorts provided none of the features?
10

 

Let me know if you have any questions, and if you're set, thanks for accepting,
Scott