Question

A certain school has 60 teachers. Of these, 32 teach English, 28 teach History, 20 teachers teach geography, 15 teach English and History but no one teaches English and Geography.

i) Draw a Venn diagram to represent the given information.
ii) Find the number of teachers who teach
a) Geography and History.
b) History only

Answer 1

a) Geography and History. = 33

b) History only = 10

How to solve

Let's represent the given information using a Venn diagram for better visualization:

Let's label the sets:

E for English

H for History

G for Geography

From the information given:

Teachers who teach English (E) = 32

Teachers who teach History (H) = 28

Teachers who teach Geography (G) = 20

Teachers who teach English and History but not Geography = 15

Now, we'll fill in the Venn diagram based on this information:

Now, let's find the number of teachers who teach:

a) Geography and History.

For this, we'll use the principle of inclusion and exclusion.

Total teaching Geography (G) = 20

Total teaching History (H) = 28

Teachers teaching both Geography and History (G ∩ H) = Total(G) + Total(H) - Teaching both G and H but not E (15) = 20 + 28 - 15 = 33.

b) History only.

Teachers teaching only History = Total teaching History (H) - Teaching both History and Geography (G ∩ H) - Teaching English and History but not Geography = 28 - 33 + 15 = 10.