Questions

Out of 100 students of class V, 73 passed in Mathematics and 84 in Nepali in the final examination but 7 failed in both subjects and 5 were absent in the examination.

1. If M and N represent the set of students who passed in Mathematics and Nepali then what are the values of n(M) and n(N)?
2. Find the total number of students who failed in both subjects.
3. Find the number of students who passed in either of the subjects.
4. Find the number of students who passed in both subjects.
5. Show the given information in a Venn-diagram. Which region in the Venn-diagram represents the maximum number of students?

In a class of 65 students, 10 students liked Maths but not English, and 20 students liked English but not Maths. If 5 students did not like both then,

1. Find the number of students who liked Maths or Science.
2. Find the number of students who liked both Maths and Science.
3. Show the given information in a Venn-diagram.
4. Find the cardinality of the set representing the symmetric difference of the set of students who like Maths and Science.

In a class of 25 students, 12 have chosen Mathematics, 8 have chosen Mathematics but not Biology. If each of them has chosen at least one, then

1. What is the relation between the total number of students and the students who have not chosen Mathematics or Biology?
2. Find the number of students who have chosen both Mathematics and Biology.
3. Find the number of students who have chosen Mathematics but not Biology.
4. Find the cardinality of the set representing the symmetric difference of the set of the students who like Mathematics and Biology.

The population of the village is 15000. Among them 9000 read Magazine A, 7500 read Magazine B, and 40% read both magazines.

1. Find the percentage of $\rm n(A \cap B)$.
2. Find the value of $\rm n(A \cup B)$.
3. Find the number of people who don't read both magazines.
4. Find the percent of people who don't read both magazines.

In an exam, 70% of the examinees passed in Science, 75% in Maths, 10% of them failed in both subjects, and 220 examinees passed in both subjects. If S and M are the set of examinees passed in Science and Maths respectively, then answer the following questions:

1. Find the percentage of n(S $\rm \cup$ M).
2. FInd the percentage of n(S $\rm \cap$ M).
3. Find the total number of students.
4. What percentage in the Venn diagram has been covered by n(S $\rm \triangle$ M)?

45% of the students of a school play basketball, 40% play cricket, and 30% play both. If 360 students play neither basketball nor cricket then answer the following questions:

1. If B and C represent the sets of students who like basketball and cricket, respectively, what percentage represents $\rm n \overline { \left ( C \cup B \right )} $ in the question?
2. Find the number of students who play either basketball or cricket.
3. Find the total number of students.
4. Find the number of students who play basketball only.

In an examination, it was found that 55% failed in Maths and 45% failed in English. If 35% passed in both subjects

1. What percent failed in Maths only?
2. What percent failed in English only?
3. Represent the above information in a Venn diagram.
4. Find the percentage of students who failed in both subjects.

Out of 100 students, 80 passed in Science, 71 in Mathematics, 10 failed in both subjects, and 7 did not appear in an examination.

1. Let S and M represent the sets of students who were passed in science and Maths respectively, then find n(S) and n(M).
2. Find the number of students who passed in either Science or Mathematics.
3. Find the number of students who passed in both subjects.
4. Represent the above information in a Venn diagram.

Out of 90 civil servants, 65 were working in the office, 50 were working in the field and 35 were working in both the premises (sites).

1. Let O and F represent the set of civil servants working in office and field respectively, then find $\rm n(F)$ and $\rm n(O \cap F)$.
2. Represent the given information in a Venn diagram.
3. How many civil servants were absent?
4. How many civil servants were working in the field only?

In sets A and B, A has 50 members, B has 60 members, and 30 members are the same in both sets. By how many elements $\rm (A \cup B)$ is formed?