In a class,30 offer biology, 21 offer chemistry and 22 offer physics. 15 offer physics and biology,10 offer ph ysics and chemistry and 13 offer biology and chemistry. 2 offer physics only,3 offer chemistry only and 7 offer biology only. i. Illustrate this information in a Venn diagram ii.
To illustrate this information in a Venn diagram, we can represent the three subjects (biology, chemistry, and physics) with three overlapping circles.
First, we label the circles for each subject: "Biology," "Chemistry," and "Physics."
ii. To fill in the Venn diagram with the given information, we start with the information provided.
- 30 students offer biology, so we place the number 30 in the Biology circle.
- 21 students offer chemistry, so we place the number 21 in the Chemistry circle.
- 22 students offer physics, so we place the number 22 in the Physics circle.
Next, we move on to the students who offer more than one subject:
- 15 students offer both physics and biology, so we place the number 15 in the overlapping region between the Physics and Biology circles.
- 10 students offer both physics and chemistry, so we place the number 10 in the overlapping region between the Physics and Chemistry circles.
- 13 students offer both biology and chemistry, so we place the number 13 in the overlapping region between the Biology and Chemistry circles.
Finally, we consider the students who offer only one subject:
- 2 students offer physics only, so we subtract the number of students who offer both physics and another subject (10 students) from the total number of students who offer physics (22 students). Hence, we place the number 12 in the region outside the overlap between Physics and any other circle.
- 3 students offer chemistry only, so we subtract the number of students who offer both chemistry and another subject (13 students) from the total number of students who offer chemistry (21 students). Hence, we place the number 8 in the region outside the overlap between Chemistry and any other circle.
- 7 students offer biology only, so we subtract the number of students who offer both biology and another subject (15 students) from the total number of students who offer biology (30 students). Hence, we place the number 15 in the region outside the overlap between Biology and any other circle.
The resulting Venn diagram would have the numbers as described above, illustrating the given information about the number of students offering each subject and the overlaps between subjects.