Question

In a class of 35 students, 20 offer Physics, 18 offer Chemistry and 2 offer neither Physics nor Chemistry. i) Illustrate the information on a Venn diagram. ii) How many students offer all the two subjects? ii) How many students offer Physics? iv) How many students offer only one subject?​

Answer 1

Answer:

Given:

• 35 = Total number of students
• 20 = Physics students
• 18 = Chemistry students
• 2 = Neither Physics or Chemistry students

To construct the Venn diagram:

• Draw 2 circles overlapping.  
  Label one P (for Physics) and the other C (for Chemistry)

• Draw a box around the circles.

As 2 students study neither subject, place the number 2 in the box outside the circles.

Calculate the number of students who study both subjects (central overlapping section):

Physics students + Chemistry students + neither students - Total students

= 20 + 18 + 2 - 35 = 5

Place the number 5 in the central overlapping section.

⇒ Left section = Physics students - both subjects

                        = 20 - 5

                        = 15

⇒ Right section = Chemistry students - both students

                          = 18 - 5

                          = 13

i) See attachment

ii) Physics and Chemistry = 5 students

iii) Physics only = 15 students

iv) One subject only = 15 + 13 = 28 students