venn diagram solving for 3 students likes geography physics science 75 likes only one subject 65 likes exactly two 15 like all three.1)how many students in a class
2)how many students like atleast one
3)how many students like only physics
4)how many students like only geography
5)how many students like only geography and physics
39
To solve this problem using a Venn diagram, we can follow these steps:
Step 1: Create a Venn diagram with three overlapping circles representing the three subjects: geography (G), physics (P), and science (S).
Step 2: Fill in the given information:
- Let the number of students who like all three subjects be x = 15.
- Let the number of students who like only geography be a.
- Let the number of students who like only physics be b.
- Let the number of students who like only science be c.
- Let the number of students who like both geography and physics be d.
- Let the number of students who like both geography and science be e.
- Let the number of students who like both physics and science be f.
Step 3: Fill in the remaining information based on the given data:
- 75 students like only one subject. This means a + b + c = 75.
- 65 students like exactly two subjects. This means d + e + f = 65.
Now, let's solve the questions:
1) To find the total number of students in the class, we need to find the sum of all the regions in the Venn diagram. It can be represented as:
Total students = a + b + c + d + e + f + x + (students who like at least two subjects but not all three)
2) To find the number of students who like at least one subject, we need to find the sum of all the regions except the empty set:
Students who like at least one subject = a + b + c + d + e + f + x
3) To find the number of students who like only physics, we need to find b.
4) To find the number of students who like only geography, we need to find a.
5) To find the number of students who like only geography and physics, we need to find d.
To find the values for a, b, c, d, e, and f, we need more information about the overlapping regions or the total number of students.