Back to: O level mathematics notes syllabus uganda

The following examples will illustrate how a Venn diagram can be used

to solve certain mathematical problem.

Example

Use Venn diagram to show that:

a) (A n B)’ = A’ U B’

b) (A u B)’ = A’ n B’

**Example**

There are 40 men working in a company. 38 of them own either a car

or a house or both. 33 men own a car, 24 of whom also own a house.

Represent this information in a Venn diagram and use it to state:

a) the number of men who do not own a house.

b) the number of men who own a house but do not own a car.

c) the number of men who own neither a car nor a house.**Solution**

Let, C represent those who own a car.

H represents those who own a house.

And let: x be the number of men who own a car only.

y be the number of men who own a house only.

Z be the number of men who own neither a car nor a house.

Given:

n(ℇ) = 40

n(C U H) = 38 ,n(C) = 33

n(C n H) = 24, n(H) = ?

From the diagram:

X + 24 = 33

X = 33 – 24 = 9

n(C U H) = X + 24 +y = 38

9 + 24 +y = 38

y = 5

a) Number of men who do not own a house

n (H) =x + Z = 9 + 5 = 14

b) Number of men who own a house but not a car = y = 5

c) n(C’ U H’) = Z =2