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In Mathematics / Middle School | 2014-04-30

A survey of 80 sophomores at a certain western college showed that:

- 36 take English
- 32 take History
- 32 take Political Science
- 16 take both History and English
- 16 take both Political Science and History
- 14 take both Political Science and English
- 6 take all three courses

How many students:

1. Take English and neither of the other two?
2. Take none of the three courses?
3. Take History but neither of the other two?
4. Take Political Science and History but not English?
5. Do not take Political Science?

Asked by trelonniaboyce

Answer (3)

The number of students in these five cases will be 12, 20, 6, 10, and 24, respectively.
What are Sets?
Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
A survey of 80 sophomores at a certain western college showed below.

36 take English
32 take history
32 take political science
16 take history and English
16 take political science and history
14 take political science and English
6 take all three

The circle diagram is given below.

The number of students who take English and neither of the other two will be 12.
The number of students who take none of the three courses will be 20.
The number of students who take a history , but neither of the other two will be 6.
The number of students who take political science and history but not English will be 10.
The number of students who do not take political science will be 24.

More about the sets link is given below.
https://brainly.com/question/8053622
#SPJ2

Answered by jainveenamrata | 2024-06-16

1. take English and niether of the other two? 36-6 that we know take all 3 This leave 30. Subtract the 6 from those taking history and English. Leaves 10. Subtract the 10 from those taking English. This leaves 20. Subtract the 6 from those taking political science and English. Leaves 8. Subtract 8 from those taking English. Leaves 12 2. take none of the three courses? 3. take history, but niether of the other two Do the same with history as we did with English. 32-6 = 26 -10=16-10= 6 4. take political science and history but not english 16-6 (that take all 3) = 10
Hope at least the partial answer helps!

Answered by lemondropfan64 | 2024-06-24

The answers to the questions are as follows: 1) 12 students take English and neither of the other two; 2) 20 students take none of the three courses; 3) 6 students take History but neither of the other two; 4) 10 students take Political Science and History but not English; 5) 48 students do not take Political Science.
;

Answered by jainveenamrata | 2024-12-20

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