In a group of 1000 people, there are 750 people will speak English and 400 people will speak Russian. How many may speak English only? How many will speak Russian? How many can speak both English and Russian?

Solution:              Total number of people = 1000

                n (E) = 750

                n (R) = 400

                n (E υ R) = n (E) + n (R) - n (E ∩R)

                n (E ∩ R) = 750 + 400 - 1000

                = 150 speaking English and Russian both.

                People speaking only English = n (E) - n (E∩R) = 750 - 150 = 600

                People speaking only Russian = n (R) - n (E∩ R) = 400 - 150 = 250.