Swati Lathia

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Video Examples – Word Problems in Set

Example 1

If A & B are two sets such that n(A)=17, n(B)=23, n(AUB) = 38. Then Find n (A ∩ B).

Example 2

If A & B are two sets such that A has 12 elements , B has 17 elements, A U B has 21 elements, how many elements does A ∩ B have?

Example 3

If n(U) = 700, n(A) = 200, n(B) = 300, n (A ∩ B) = 100. Find n (A’ U B’).

Example 4

In a committee, 50 people speak Gujarati, 20 speak English & 10 speak both Gujarati & English. How many people speak at least one of these two languages?

Example 5

In a group of 70 people, 45 speak Gujarati language and 33 speak English language and 10 speak neither Gujarati nor English. How many people can speak both English as well Gujarati language? How many can speak only English language?

Example 6

In a class of 50 students, 35 opted for Mathematics (M), 37 opted for Economics (E). How many students have opted for both Mathematics & Economics? How many students have opted for only Mathematics? Here, assume that each student has to opt for at least one of the two subjects.

Example 7

In a city, 3 daily newspapers A, B, C are published. 42% of the people in a city, read A. 51% read B. 68% read C. 30% read A & B. 28% read B & C. 36% read A & C. 8% do not read any of the three newspapers. Find the percentage of person who read all three newspapers.

Example 8

In a group of 100 people, 65 like to play cricket (C), 40 like to play tennis (T), 55 like to play volley ball (V). All of them like to play at least one of three games. If 25 like to play both cricket and tennis, 24 like to play both tennis and volley ball and 22 like to play both cricket and volley ball, then how many like to play all three games? How many like to play cricket only? How many like to play tennis only?

Example 9

In a village with a population of 5000, 3200 people are egg-eaters, 2500 meat eater and 1500 eat both egg and meat. How many people in the village are pure vegetarians?

Example 10

In a class, 22 students offered Mathematics, 18 students offered Accountancy and 24 students offered Statistics. All of them have to offer at least one of the three subjects. 11 are in both Mathematics and Accountancy, 13 in Accountancy and Statistics, 14 are in Mathematics and Statistics and 7 have offered all three subjects. Find (i) How many students are there in class? (ii) How many students offered only Mathematics?

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