Exercise To Do (Three Sets)

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  1. In a survey of 330 people about religion perferences, 40 believe in Hindu only religion, 50 believe in Buddhism only and 60 in other religion only. Among them 65 don't find any difference in Hindu and Buddhism, 55 don't find any difference in Hindu and other religion and 75 don't find any difference between Buddhism and other religions. If 25 don't believe in any religion.
    1. Write the given information in set notation.
    2. Find out how many do not find any difference in any religion.
    3. Identify the number of people who don't find any difference between Hindu religion and Buddhism.
    4. Compare the number who believe in exactly one religion and exactly two religion.
  2. In a survey among college students regarding their preferences to build library, cafeteria, and park, 10% liked the library only, 15% liked cafeteria only and 25% liked park only. Similarly, 20% like any of them. Likewise, 25% liked the library and cafeteria, 30% liked cafeteria and park and 28% liked library and park.
    1. Write the given information in set notation.
    2. How many students like none of three things?
    3. Find the percentage of students who like libraries or cafeterias.
    4. What percentage of the students liked the library or cafeteria but not park?
  3. In a competition of 80 students, medals were awarded in different categories. Among them, 5 medals were in only dance, 6 medals were in only dramatics and 7 medals were in only music. A total of 70 students received the medals and only 6 student got medals in all the three categories.
    1. Write the cardinality notation to represent who did not receive medals.
    2. Illustrate the above information in a Venn diagram.
    3. How many received medals in exactly two of these categories?
    4. If the school distributed the medals to 20% students, find the number of students.
  4. In a survey conducted on students studying in grade 10 at Shree Sharada Secondary School to determine suitable place for educational trips among Pokhara, Lumbini and ilam, it was found that 40 students considered Pokhara to be suitable, 30 students considered Lumbini to be suitable, and 45 students considered Ilam to be suitable. While 15 students of that grade said that all three places are suitable, 5 students did not express any opinion, and no one likes only two places. [CDC Model Question 2080)
    1. If P, L , I denote the set of students who prefer Pokhara, Lumbini and Ilam respectively, write the cardinality notation of students for whom all places are suitable.
    2. Illustrate the above information in a Venn diagram.
    3. How many students are studying in grade 10 in the Sharada Secondary School?
    4. If 5 students, who did not express their opinion in the survey had said Lumbini as a suitable place, then what would have been the ratio of students who considered only Pokhara was the suitable place and only Lumbini was the suitable place?
  5. In a survey of 180 people, it was found that 80 read Newspaper A, Newspaper B, Newspaper C, 25 read Newspaper A and B, 20 read Newspaper A and Newspaper C, 25 read Newspaper B and C and 5 read all three newspapers.
    1. Write the cardinality of universal set.
    2. How many people didn't read all three newspapers?
    3. How many read exactly two newspaper?
    4. What percentage of people read newspapers A or B but not C?
  6. In a survey of 120 people, it was found that 40 eat Apple, 40 eat Banana, 55 eat Mango, 10 eat Apple as well as Banana, 20 eat Apple as well as Mango, 15 eat Banana as well as Mango and 5 eat all three fruits.
    1. If A, B and M denote the set of people who eat Apple, Banana and Mango respectively, what does \(n(A \cap B \cap M)\) denote?
    2. Express the above information in a Venn-diagram.
    3. Find the value of \(n(A \cup B \cup M)\).
    4. How many people like exactly one fruits?
  7. In an examination, 50% students secured A+ grades in Mathematics, 40% in Science, 60% in Nepali, 15% in Mathematics and Science, 20% in Science and Nepali and 25% in Nepali and Mathematics. If every student obtained A+ grade at least in one subject.
    1. Write the set notation for the cardinality of set of students who secured A+ grades in Mathematics or Science or Nepali.
    2. Illustrate the above information in a Veno-diagram.
    3. Find the percentage of students who secured A+ grades in all the three subjects.
    4. If the number of students who secured A+ grades at least in two subject is 120 then find the number of students who secured A + grades in at most two subjects.
  8. In an exam of English language test, 25 passes in reading or writing, 3 passes in speaking only and 8 failed in all the three tests.
    1. If R, W, L represent the test reading, writing and speaking then write the formula of \(n \cup E \cup H\).
    2. Illustrate the above information in a Venn diagram.
    3. How many people were asked this question?
    4. If 7 students pass all three tests, then how many students passed at most two tests?
  9. In a dance academy, among the three dances Deuda Nach, Maruni Nach and Lakhe Nach, 39 students dance only one kind, 48 students dance only two kind and every student dances at least one kind.
    1. If D, M and L respectively denote the set of students who dance Deuda Nach, Maruni Nach and Lakhe Nach then write value of students who dance in all three in terms of x.
    2. Draw a Venn-diagram to show the above information.
    3. How many students dance at most two kind?
    4. If the tudents participated in Deuda Nach, Maruni Nach and Lakhe Nach are in the ratio 1:2:3, then how many student dance in Deuda Nach.
  10. In a survey of 100 people, 10 liked only Nepali films, 15 liked only English films, 18 liked only Hindi films, 38 liked exactly two films, and 14 liked none of the films.
    1. If N, E, H represent the sets of people who like Nepali, English and Hindi films respectively then write the formula of \(N \cup E \cup H\).
    2. Illustrate the above information in a Venn diagram.
    3. How many people liked all the three films?
    4. Compare the number who like at least one and at least twi films.
  11. In a class, every student likes volleyball or football or cricket. The ratio of students who like (volleyball or football) and only cricket is 9:1, and 10 like all the three game.
    1. Write the given information in set notation in terms of x.
    2. Illustrate the above information in a Venn diagram.
    3. Find the percent of students who like volleyball or football.
    4. If the number of students who like at lest one and at most two and are in the ratio 10:9, then find the number of total students.

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