11 Out of a group of 70 people, 37 people like Hindi movies, 52 like English movies and each person likes at least one of the two movies. Find the number of people who like:
(a) both the movies (b) only English movies
12. In a village there are 850 people who speak Hindi or Bengali. Out of these 675 people speak Hindi and 200 people speak both the languages. How many people speak Bengali? How many people speak only Hindi?
DO STEPBY STEP FAST PLZ
Answers
Step-by-step explanation:
We will first consider that the people who like coffee are represented as P and the people who like tea will be denoted by Q.
According to the question, we have that there is a group of 70 people. That is the total number of people is 70 and this can be written as n(P ∪∪ Q) = 70.
We are given that the number of people who like coffee is 37. So, we actually have n(P) = 37. Moreover we have a number of people who like to drink tea. Therefore, we can write it as n(Q) = 52.
We are supposed to find out the number of people who like both coffee and tea. That is, we need to find the value of n(P ∩∩ Q). Since all the values are finite values therefore we will apply here the formula of cardinal property which can be written as n(P ∪∪ Q) = n(P) + n(Q) - n(P ∩∩ Q). Here n represents numbers of the particular set.
After substituting the values we have 70 = 37 + 52 - n(P ∩∩ Q). By taking all the numbers to the left hand side of the equal sign we have 70 - 37 - 52 = - n(P ∩∩ Q).
Therefore the value of - n(P ∩∩ Q) is -19. Or by cancelling the minus sign from both the sides we have n(P ∩∩ Q) = 19.
The Venn diagram for the question is shown below along with U representing a universal set.