There are 40 pupils in a class 30 of them study biology,22 study physics and 21 study chemistry.15 study physics and biology,10 study physics and chemistry and 13 study biology and chemistry.each student in the class studies at least one of the three subject.represent it on a venn diagram
If x take all three, then
30+22+21 - (15+10+13) + x = 40
x = 5
so in your Venn diagram, place a 5 in the middle spot.
Then subtract 5 from each of the two-subject spots
then place the remainder in the large single-subject spots.
Go google 3-way Venn diagrams ...
Please show workings
Haven't solve all
To represent this information on a Venn diagram, we need to create three overlapping circles, one for each subject: Biology, Physics, and Chemistry.
1. Start by drawing three overlapping circles that intersect in the center.
2. Label the three circles as Biology, Physics, and Chemistry.
3. Since there are 40 pupils in total and each student studies at least one of the three subjects, place the value 40 in the universal set outside the circles.
4. Now, fill in the numbers given for the overlapping regions.
- Place 30 in the Biology circle, as 30 students study biology.
- Place 22 in the Physics circle, as 22 students study physics.
- Place 21 in the Chemistry circle, as 21 students study chemistry.
5. Fill in the remaining numbers for the overlapping regions based on the given information.
- 15 students study Physics and Biology, so place this value in the intersection of the Biology and Physics circles.
- 10 students study Physics and Chemistry, so place this value in the intersection of the Physics and Chemistry circles.
- 13 students study Biology and Chemistry, so place this value in the intersection of the Biology and Chemistry circles.
6. Finally, fill in the remaining overlapping region in the center, which represents the students who study all three subjects.
Based on the given information, we can calculate the value using the formula:
Total students in the overlapping region = Total students in Biology + Total students in Physics + Total students in Chemistry - (Students in Biology and Physics + Students in Physics and Chemistry + Students in Biology and Chemistry)
Total students in the overlapping region = 30 + 22 + 21 - (15 + 10 + 13)
Total students in the overlapping region = 30 + 22 + 21 - 38
Total students in the overlapping region = 75 - 38
Total students in the overlapping region = 37
Place the value 37 in the center of the Venn diagram.
Now, you have successfully represented the given information on a Venn diagram.