# Solve: Sets and Venn Diagrams

Please view the attachment to see questions 1 and 2.

3. A survey of 10355 people restricted to those who were either female or Hispanic or over 16 years of age, produced the following data:

Female: 6022 Hispanic female: 2136

Hispanic: 3564 Over 16 and female: 959

Over 16: 4722 Over 16 and Hispanic: 1341

Hispanic female over 16: 239

Is the data consistent? If not, why?

4. The following Venn diagram (please view the attached file) illustrates the number of seniors (S), male students (M), and students on the dean's list (D) at a small private college. Describe each number.

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1. Use Venn diagrams to illustrate the following sets:

(a) A′ ∩ B

(b) (A′ ∩ B′) U C

(c) A ∩ (A U B)

(d) A U (A ∩ B)

(e) (A U B) ∩ (A U C)

2. Use Venn diagrams to ...

#### Solution Summary

This solution is provided in an attached Word document. All required diagrams are included.

11 Problems on Sets and Venn Diagrams

1. Given the venn diagram, find P ∩ Q. Write in correct set notation.

[Please refer to the attachment for the Venn diagram]

2. 2. Write down all possible subsets of set P using correct set notation.

[Please refer to the attachment for the Venn diagram]

3. The cardinal number of the set {triangle, rectangle, square, trapezoid, octagon, rhombus, circle, ellipse, pentagon} is _________.

4. Given the following sets, select the statement below that is true.

A = {r, i, s, k, e, d}, B = {r, i, s, e}, C = {s, i, r}

[Please refer to the attachment for the questions]

5. Without writing them all out, what is the number of subsets of set A = {king, queen, knight, prince, princess, duke}?

6. Given the following set, select the statement below that is true.

V = {a, e, i, o, u}

[Please refer to the attachment for the questions]

7. Given these sets:

A = {1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

C = {3, 5, 7, 9}

List the elements of the set B U (A ∩ C)

Show your work, step by step.

8. The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 28 said they had taken physics, 47 said they had taken chemistry and 13 said they had taken both. Twelve said they had taken neither. How many recent high school grads were surveyed?

9. The President's Council on Fitness asked adults who exercise if they walk, run or stretch. Here is the Venn diagram of the results. Of those adults surveyed, how many ran but did not stretch?

[Please refer to the attachment for the Venn diagram]

10. A charity asked people attending a fundraiser cookout if they ate the salad, casserole or dessert. Here is the Venn diagram of the results. Of those surveyed, how many people ate dessert and casserole?

[Please refer to the attachment for the Venn diagram]

11. The Wildlife Federation surveyed 170 San Diego residents. The results are as follows:

26 had a membership to the Birch Aquarium

44 had a membership to the San Diego Zoo

17 had both

Construct a Venn diagram and answer the following questions:

i. How many had only a zoo membership?

ii. How many had only an aquarium membership?

iii. How many belonged to either one or the other or both?

iv. How many belonged to neither?

[Please refer to the attachment for details]

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