# Week 2 Assignment 2 Mixed Problems

See attached file for full problem description.

1. If A  B and B  C, what can you conclude? Why? What if A  B and B  C? If A  B and B  C?

2. Write down all possible subsets of {a, b, c, d}

3. Without writing them down what are the number of subsets of the set A = {a, b, c, d, e, f}? Of set B = {a, b, c, d, e, f, g, h, i, j}?

4. Given U = {All letters of the alphabet} A = {b, c, d} and B = {c, e, f, g}

List the elements of set

(a) A U B (b) A ∩ B (c) A′ ∩ B′ (d) A′ U B′ (e) A U B′

(f) (A U B′ ) ∩ B (g) (A U B) ∩ (A U B′)

5. Write the following in roster form: Set J is the set of natural numbers between one and seven.

6. State whether set A and B are equal, equivalent, both, or neither.

A = {9, 8, 10} B = {8, 9, 10}

7. Express the following in set-builder notation: M = {1, 2, 3, 4, 5}

8. A drug company is considering manufacturing a new product that has two different flavors, orange and cherry. They surveyed 120 people. The results are as follows:

62 liked cherry flavor, 74 liked orange flavor, 35 liked both flavors.

Construct a Venn diagram and answer the following:

a) How many liked only orange flavor?

b) How many liked only cherry flavor?

c) How many liked either one or the other or both?

9. In a survey of 75 resorts, it was reported that:

34 provided refrigerators in the guest rooms

30 provided laundry services

37 provided business centers

15 provided refrigerators in the guest rooms and laundry services

17 provided refrigerators in the guest rooms and business centers

19 provided laundry services and business centers

7 provided all three features.

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

(a) How many of the resorts provided only refrigerators in the guest rooms?

(b) How many of the resorts provided exactly one of the features?

(c) How many of the resorts provided at least one of the features?

(d) How many of the resorts provided exactly two of the features?

(e) How many of the resorts provided none of the features?

#### Solution Preview

Please see attached file.

1.

Solution:

A B represents that A is the subset of B, which means that every element of the set A belongs to set B.

A B represents that A is the proper subset of B, which means that every element in the Set A belong to set B and at least one element of B will not be in the set A.

Now we have A B and B C, every element in set A belongs to set B and every element in set B belongs to set C. So we can conclude that every element in Set A belongs to Set C i.e. If A B and B C then A C. If A B and B C then A C. If A B and B C implies A C, since here A is the subset of B and B is the proper subset of C then we can say that A will be the proper subset of C.

2.

Solution:

The subset of {a, b, c, d} are {a}, {b}, {c}, {a, b}, {a, c}, {a, d}, {b, c} {b, d}, ...

#### Solution Summary

This solution looks at determining the subsets and probabilities for the statistics problems.