Venn Diagrams

Help Questions

ACT Math › Venn Diagrams

Questions 1 - 10
1

Venn diagram

In the venn diagram above, let the set and let , what is the set Use set notation to enumerate your answer.

Explanation

means the intersection of the sets and , the only things in the intersection are elementes that are in BOTH of the sets. Since there is nothing shared by the two sets (no elements are in both), the interesction is the emptyset, or:

2

Venn diagram

In the venn diagram above, let the set and let , what is the set Use set notation to enumerate your answer.

Explanation

means the intersection of the sets and , the only things in the intersection are elementes that are in BOTH of the sets. Since there is nothing shared by the two sets (no elements are in both), the interesction is the emptyset, or:

3

Venn diagram

In the venn diagram above, let the set and let , what is the set Use set notation to enumerate your answer.

Explanation

means the intersection of the sets and , the only things in the intersection are elementes that are in BOTH of the sets. Since there is nothing shared by the two sets (no elements are in both), the interesction is the emptyset, or:

4

Set A contains the positive even integers less than 14. Set B contains the positive multiples of three less than 20. What is the intersection of the two sets?

A∩B = { }

A∩B = {6, 12}

A∩B = {4, 6, 8}

A∩B = {6}

A∩B = {6, 12, 18}

Explanation

A = {2, 4, 6, 8, 10, 12}

B = {3, 6, 9, 12, 15, 18}

The intersection of a set means that the elements are in both sets: A∩B = {6, 12}

5

Set A contains the positive even integers less than 14. Set B contains the positive multiples of three less than 20. What is the intersection of the two sets?

A∩B = { }

A∩B = {6, 12}

A∩B = {4, 6, 8}

A∩B = {6}

A∩B = {6, 12, 18}

Explanation

A = {2, 4, 6, 8, 10, 12}

B = {3, 6, 9, 12, 15, 18}

The intersection of a set means that the elements are in both sets: A∩B = {6, 12}

6

Set A contains the positive even integers less than 14. Set B contains the positive multiples of three less than 20. What is the intersection of the two sets?

A∩B = { }

A∩B = {6, 12}

A∩B = {4, 6, 8}

A∩B = {6}

A∩B = {6, 12, 18}

Explanation

A = {2, 4, 6, 8, 10, 12}

B = {3, 6, 9, 12, 15, 18}

The intersection of a set means that the elements are in both sets: A∩B = {6, 12}

7

In a class of senior high-school students, have pet cats, have pet dogs, have both cats and dogs, and have neither cats nor dogs. How many total students are in the class?

Explanation

A Venn diagram can help us determine the total number of students in the class.

First, we must calculate the number of students who have ONLY cats or ONLY dogs. First, for cats, 15 students have cats, and 5 students have both cats and dogs.

Ten students have only cats.

For dogs, 12 students have dogs, and 5 students have both cats and dogs.

Seven students have only dogs.

Using this information, we can fill in the Venn diagram.

Venn_4

This diagram shows the 10 students with only cats, the 7 students with only dogs, the 5 students with both, and the 8 students with neither. Adding up the numbers will give us the total number of students.

8

In a class of senior high-school students, have pet cats, have pet dogs, have both cats and dogs, and have neither cats nor dogs. How many total students are in the class?

Explanation

A Venn diagram can help us determine the total number of students in the class.

First, we must calculate the number of students who have ONLY cats or ONLY dogs. First, for cats, 15 students have cats, and 5 students have both cats and dogs.

Ten students have only cats.

For dogs, 12 students have dogs, and 5 students have both cats and dogs.

Seven students have only dogs.

Using this information, we can fill in the Venn diagram.

Venn_4

This diagram shows the 10 students with only cats, the 7 students with only dogs, the 5 students with both, and the 8 students with neither. Adding up the numbers will give us the total number of students.

9

In a class of senior high-school students, have pet cats, have pet dogs, have both cats and dogs, and have neither cats nor dogs. How many total students are in the class?

Explanation

A Venn diagram can help us determine the total number of students in the class.

First, we must calculate the number of students who have ONLY cats or ONLY dogs. First, for cats, 15 students have cats, and 5 students have both cats and dogs.

Ten students have only cats.

For dogs, 12 students have dogs, and 5 students have both cats and dogs.

Seven students have only dogs.

Using this information, we can fill in the Venn diagram.

Venn_4

This diagram shows the 10 students with only cats, the 7 students with only dogs, the 5 students with both, and the 8 students with neither. Adding up the numbers will give us the total number of students.

10

There are 75 juniors at a high school. 15 of the students are enrolled in Physics and 40 students are enrolled in Chemistry. 30 students are not enrolled in either Physics or Chemistry. How many students are enrolled in both Physics and Chemistry?

30

25

15

10

5

Explanation

First, subtract the students that are in neither class; 75 – 30 = 45 students.

Thus, 45 students are enrolled in Chemistry, Physics, or both. Of these 45 students, we know 40 are in Chemistry, so that leaves 5 students who are enrolled in Physics only; with 15 total students in Physics, that means 10 must be in Chemistry as well. So 10 students are in both Physics and Chemistry.

Page 1 of 5
Return to subject