In class of 200 students 70 offered physics 90 chemistry 100 mathematics while 24 did not offer any of the three subjet.23 students offered physic and chemistry 41 chemistry and mathematics while 8 offered all three subjet.draw avenn diagram to illustrate the information
Draw your Venn diagram and review its properties. If x offered physics and math, then
70+90+100 - (23+41+x) + 8 = 200-24
Cannot diagram on these posts.
To draw a Venn diagram to illustrate the given information, we will first start by labeling the three circles representing the subjects: Physics, Chemistry, and Mathematics.
Based on the given information, we can start filling in the values. Let's go step by step:
1. There are 200 students in total, and 24 of them did not offer any of the three subjects. So, we write 24 outside all three circles.
2. 70 students offered Physics, so we write 70 inside the Physics circle.
3. 90 students offered Chemistry, so we write 90 inside the Chemistry circle.
4. 100 students offered Mathematics, so we write 100 inside the Mathematics circle.
5. 23 students offered Physics and Chemistry, so we write 23 in the overlapping region between the Physics and Chemistry circles.
6. 41 students offered Chemistry and Mathematics, so we write 41 in the overlapping region between the Chemistry and Mathematics circles.
7. 8 students offered all three subjects, so we write 8 in the region where all three circles overlap.
After incorporating all the given information, the Venn diagram would look like this:
```
_____
/ \
| P: 70 |
\_____/
_____
/ \
| C: 90 |
\_____/
_____
/ \
| M: 100 |
\_____/
```
Now let's fill in the overlapping regions:
```
_____
/ \
| P: 70 |
\___|____
| \
_____ |
/ \ |
| C: 90 | |
\___|____/
| \
_____ |
/ \ |
| M: 100 | |
\___|____/
| \
|_____\
8
```
Here, P represents Physics, C represents Chemistry, and M represents Mathematics. The numbers inside the circles indicate the number of students taking each subject, and the number outside the circles represents the students taking none of the subjects.
To draw a Venn diagram, we need to determine the overlapping portions and the numbers of students in each section.
Let's start by labeling the three circles for Physics (P), Chemistry (C), and Mathematics (M).
Given information:
- Total students in the class = 200
- Students not offering any of the three subjects = 24
- Students offering Physics and Chemistry = 23
- Students offering Chemistry and Mathematics = 41
- Students offering all three subjects = 8
Using this information, we can calculate the student counts for each section of the Venn diagram:
1. Students offering Physics only (P) = Number of students offering Physics (P) - Number of students offering Physics and Chemistry (P∩C) - Number of students offering all three subjects (P∩C∩M)
P = 70 - 23 - 8 = 39
2. Students offering Chemistry only (C) = Number of students offering Chemistry (C) - Number of students offering Physics and Chemistry (P∩C) - Number of students offering all three subjects (P∩C∩M)
C = 90 - 23 - 8 = 59
3. Students offering Mathematics only (M) = Number of students offering Mathematics (M) - Number of students offering Chemistry and Mathematics (C∩M) - Number of students offering all three subjects (P∩C∩M)
M = 100 - 41 - 8 = 51
Now we can label the respective sections of the Venn diagram:
- Students offering Physics only (39) -> Label it as P
- Students offering Chemistry only (59) -> Label it as C
- Students offering Mathematics only (51) -> Label it as M
- Students offering Physics and Chemistry (23) -> Label it as P∩C
- Students offering Chemistry and Mathematics (41) -> Label it as C∩M
- Students offering all three subjects (8) -> Label it as P∩C∩M
- Students not offering any of the three subjects (24) -> Outside the circles
Please note that the numbers mentioned above may vary depending on how the question is interpreted.