Question

use the following information to fill in the venn diagram below. 100 people were asked if they liked math, science, or social studies. everyone answered that they liked at least one. 56 like math 43 like science 35 like social studies 18 like math and science 10 like science and social studies 12 like math and social studies 6 like all three subjects 10. how many people like only math? 11. how many people like only science? 12. how many people like only social studies?

Explanation:

Step1: Calculate the number of people who like only math

The formula for the number of people who like only math is \(n(\text{only math})=n(\text{math})-n(\text{math and science})-n(\text{math and social studies}) + n(\text{all three})\).
Substitute the values: \(n(\text{math}) = 56\), \(n(\text{math and science})=18\), \(n(\text{math and social studies}) = 12\), \(n(\text{all three})=6\).

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Step2: Calculate the number of people who like only science

The formula for the number of people who like only science is \(n(\text{only science})=n(\text{science})-n(\text{math and science})-n(\text{science and social studies})+n(\text{all three})\).
Substitute the values: \(n(\text{science}) = 43\), \(n(\text{math and science})=18\), \(n(\text{science and social studies}) = 10\), \(n(\text{all three})=6\).

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Step3: Calculate the number of people who like only social studies

The formula for the number of people who like only social studies is \(n(\text{only social studies})=n(\text{social studies})-n(\text{math and social studies})-n(\text{science and social studies})+n(\text{all three})\).
Substitute the values: \(n(\text{social studies}) = 35\), \(n(\text{math and social studies}) = 12\), \(n(\text{science and social studies}) = 10\), \(n(\text{all three})=6\).

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Answer:

1. \(32\)
2. \(21\)
3. \(19\)