Question

reading a venn diagram
use the diagram to solve each problem.

1. the diagram below shows the game consoles students owned.
2. the diagram below shows the pets students in a class owned.

how many people did not own both a ps4 and a xbox?
how many people had only a cat?

1. the diagram below shows the types of computers students owned.
2. the diagram below shows the classes students are taking.

how many students owned a laptop computer?
how many students are not taking both music and drama?

1. the diagram below shows the gender of students siblings.
2. the diagram below shows the attributes of flowers in a flower shop.

how many students had both a brother and a sister?
how many flowers were only red?

Explanation:

Step1: Analyze Venn Diagram for Problem 1

The total number of people is \(9 + 13+8=30\). The number of people who own both (the intersection) is \(13\). So the number of people who do not own both is \(30 - 13 = 17\).

Step2: Analyze Venn Diagram for Problem 2

The part of the cat - circle that does not overlap (only cat) is \(14\).

Step3: Analyze Venn Diagram for Problem 3

The number of students who own a laptop is the sum of the part of the laptop - circle that does not overlap (\(13\)) and the intersection (\(13\)), so \(13+13 = 26\).

Step4: Analyze Venn Diagram for Problem 4

The total number of students is \(8 + 17+19=44\). The number of students who take both (the intersection) is \(17\). So the number of students who do not take both is \(44 - 17=27\).

Step5: Analyze Venn Diagram for Problem 5

The intersection of the brother - circle and sister - circle (students who have both) is \(7\).

Step6: Analyze Venn Diagram for Problem 6

The part of the red - circle that does not overlap (only red) is \(17\).

Answer:

1. \(17\)
2. \(14\)
3. \(26\)
4. \(27\)
5. \(7\)
6. \(17\)