In a class of 32 students,22 offer mathematics, 18 offer chemistry and 16 offer physics.6 offer all the three subjects, 3 offer physics and chemistry only and 5 offer physics only.each student offers at least one subject. Illustrate the information in a Venn diagram fine the number of students who offer
1) chemistry only.
2) only one subject.
3) only two subjects.
To illustrate the information given in a Venn diagram, we will create three overlapping circles. Each circle represents a subject: mathematics, chemistry, and physics. The overlapping regions will represent the students who offer more than one subject. Let's go step by step:
Step 1: As there are 32 students in total, write this number outside the boundary of the circles.
Step 2: Since 22 students offer mathematics, write this number in the mathematics circle.
Step 3: Since 18 students offer chemistry, write this number in the chemistry circle.
Step 4: Since 16 students offer physics, write this number in the physics circle.
Step 5: We know that 6 students offer all three subjects, so write this number in the overlapping region of all three circles.
Step 6: We know that 3 students offer only physics and chemistry. Since these students are already accounted for in the overlapping region of physics and chemistry, there is no need to write this number again.
Step 7: We know that 5 students offer only physics. Write this number in the physics circle but outside the overlapping regions.
Now that we have represented the information in a Venn diagram, let's find the number of students who offer:
1) Chemistry only: This can be determined by considering the students who offer chemistry but do not offer any other subjects. Looking at the Venn diagram, we can count the number of students in the chemistry circle but outside the overlapping regions. In this case, that number is 10.
2) Only one subject: This includes the students who offer only mathematics, only chemistry, or only physics. By looking at the Venn diagram, we can count the number of students in each individual circle but outside the overlapping regions. In this case, that number is:
Mathematics only: 16 (students in the mathematics circle but outside the overlapping regions)
Chemistry only: 10 (students in the chemistry circle but outside the overlapping regions)
Physics only: 5 (students in the physics circle but outside the overlapping regions)
Hence, the total number of students who offer only one subject is 16 + 10 + 5 = 31.
3) Only two subjects: This includes the students who offer two subjects but not all three. To find this, we need to add up the number of students in each overlapping region. In this case, that number is 6 (overlapping region of all three subjects).
Hence, the total number of students who offer only two subjects is 6.
To summarize:
1) Chemistry only: 10 students
2) Only one subject: 31 students
3) Only two subjects: 6 students