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SS1: MATHEMATICS - 2ND TERM

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Topic Content:

  • Venn Diagrams & Problem Solving

Venn diagrams can sometimes be used to store numerical information.

In such cases it is also possible to use the Venn diagrams to solve problems arising from the data.

Hint:

1. Identify the sets, including the universal set.
2. Draw a Venn diagram.
3. Enter the data on the Venn diagram, starting with x, the unknown quantity.
4. Form an equation using the fact that the total number of elements in the regions equals the number of elements in the universal set.

Example 3.1.1:

In a class of 50 students, 30 study Biology and 25 study Economics, 15 study neither Biology nor Economics.

i. How many students study both subjects?
ii. How many students study Biology only?
iii. How many students Economics only?

Solution

i. Let B be the students that study Biology, and let E be the students that study Economics. Let the universal set µ be the total number of students in a class.

The information given in the question can now be rewritten as

| B | = 30, | E | = 25, | B ∩ E| = x and n(µ) = 50.

Hence number of students that study biology only n(B∩Eˊ) = 30 – x

Number of students that study Economics only n(Bˊ∩E) = 25 – x

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Total n(µ) = n(B∩Eˊ) + n(B∩E) + n(Bˊ∩E) + n(B∪E)ˊ

i.e. 50 = (30 – x) + (x) + (25 – x) + (15)

 

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