There are 60 science student in ss3 in a secondary school, 35 of whom studied chemistry, 30 studied technical dtawing, 12 of those student studied biology and chemistry, 10 studied chemistry but neither biology nor technical drawing, 11 only studied technical drawing, 10 also studied chemistry and technical drawing only
(a)how many student studied all 3 subjects
(b) how many student studied biology and technical drawing
(c)How many studied biology only
(d)draw a Venn diagram to illustrate the information
There are 60 science student in ss3 in a secondary school, 35 of whom studied chemistry, 30 studied technical dtawing, 12 of those ststudied chemistry but neither biology nor technical drawing, 11 only studied technical drawing, 10 also studied chemistry and technical drawing only
(a)how many student studied all 3 subjects
(b) how many student studied biology and technical drawing
(c)How many studied biology only
(d)draw a Venn diagram to illustrate the information
I need the answer urgently
Draw your Venn diagram. If
x studied all three
y studied only Tech & Biology
z studied only Biology
then
10+22-x = 35
11+10+y = 30
32-x+y+z = 60
Solve those, and then you can fill in the rest of the Venn diagram and answer the questions.
Pls I need the video how the question been solved. Thank you
To get the answers to the given questions, we can use the principles of set theory and Venn diagrams. Let's go step by step:
(a) To find out how many students studied all three subjects (chemistry, technical drawing, and biology), we can use the principle of inclusion-exclusion.
We know that 35 students studied chemistry, 30 studied technical drawing, and 12 studied biology and chemistry. To find the number of students who studied all three, we need to subtract the number of students who only studied chemistry (10) from the number of students who studied chemistry (35). Therefore, the number of students who studied all three subjects is 35 - 10 = 25.
(b) To find the number of students who studied biology and technical drawing, we can use a similar approach. We know that 12 students studied biology and chemistry. We also know that 10 students studied chemistry and technical drawing only. To find the commonality between biology and technical drawing, we subtract the number of students who studied chemistry and technical drawing only (10) from the number of students who studied biology and chemistry (12). Therefore, the number of students who studied biology and technical drawing is 12 - 10 = 2.
(c) To find the number of students who studied biology only, we need to subtract the number of students who studied both biology and chemistry (12) and the number of students who studied all three subjects (25) from the total number of students who studied biology. Therefore, the number of students who studied biology only is 12 - 25 = -13. However, it is not possible to have negative numbers of students, so we can conclude that there are no students who studied biology only.
(d) Based on the given information, we can now draw a Venn diagram. The three circles represent the subjects: chemistry, technical drawing, and biology. The overlapping regions represent the students who studied combinations of these subjects.
Here is a basic representation of the Venn diagram:
```
Chemistry
(35)
________
| |
| 25 | Biology
|________|
(12) /
/ (2)/
/_________/
Technical Drawing
(30)
```
In the diagram, the number inside each circle represents the number of students who studied that subject. The number in the overlapping region represents the number of students who studied the combination of subjects indicated by the overlapping circles.
Note: It's important to remember that Venn diagrams are visual tools used to represent the relationships and commonalities between sets or groups. They are not always perfectly to scale and can vary based on the information provided.