A group of students were asked whether they liked History, Science,or Geography. Their responses are as shown in the table below .

Question

All three subject=7
History and Geography=11
Geography and Science=9
History and science=10
History=34
Geography only=18
Science only =16
None of the 3 subjects=3

Answer 1

To solve this problem, we can use a Venn diagram to visualize the information given.

Let's assume that the three circles in the Venn diagram represent History, Science, and Geography.

From the given information:

- All three subjects: 7 students
We can place this number in the overlapping region of the three circles.

- History and Geography: 11 students
We can place this number in the overlapping region between the History and Geography circles.

- Geography and Science: 9 students
We can place this number in the overlapping region between the Geography and Science circles.

- History and Science: 10 students
We can place this number in the overlapping region between the History and Science circles.

- History: 34 students
We can subtract the numbers we already have from this total to find the number of students who only study History:
34 - 7 (all three) - 11 (History and Geography) - 10 (History and Science) = 6

- Geography only: 18 students
We can subtract the numbers we already have from this total to find the number of students who only study Geography:
18 - 7 (all three) - 11 (History and Geography) - 9 (Geography and Science) = -9

It seems like there's an inconsistency here, as we can't have a negative number of students studying only Geography. There might be an error in the given information.

- Science only: 16 students
We can subtract the numbers we already have from this total to find the number of students who only study Science:
16 - 7 (all three) - 10 (History and Science) - 9 (Geography and Science) = -10

Again, there's an inconsistency here with a negative number of students studying only Science. We should double-check the given information to make sure there are no errors.

- None of the three subjects: 3 students
We can place this number outside of all the circles, representing students who do not study any of the three subjects.

From the given information, we can conclude:

- The total number of students who like History is the sum of those who study History only and those who have History as one of their choices: 6 (History only) + 11 (History and Geography) + 10 (History and Science) + 7 (all three) = 34 (given total for History)
- The total number of students who like Geography is the sum of those who study Geography only and those who have Geography as one of their choices: 9 (Geography only) + 11 (History and Geography) + 18 (Geography only) + 7 (all three) = 45
- The total number of students who like Science is the sum of those who study Science only and those who have Science as one of their choices: 10 (History and Science) + 9 (Geography and Science) + 16 (Science only) + 7 (all three) = 42

However, due to the inconsistencies in the information provided, it is difficult to draw any further conclusions or determine the number of students who like each subject individually.