Question 3 - Number of elements in Set Formula - Chapter 1 Class 11 Sets

Transcript

Question 3 In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English? Let H be the set of people who speak Hindi, and E be the set of people who speak English Number of people who speak Hindi = n(H) = 250 Number of people who speak English = n(E) = 200 Total number of people = n(H ∪ E) = 400 Number of people who can speak both English and Hindi = n(H ∩ E) = ? Now, n(H ∪ E) = n(H) + n(E) – n(H ∩ E) 400 = 250 + 200 – n(H ∩ E) 400 = 450 – n(H ∩ E) n(H ∩ E) = 450 – 400 = 50 Thus, 50 people can speak both Hindi and English.