Sets MATHS - Sets

In an examination, 34% of the candidates fail in Arithmetic and 42% in English. If 20% fail in Arithmetic and English, the percentage of those passing in both subjects is:

Which of the following statements is false:

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A ∪ B ?

If A = {a, b, c},B = {c, d, e}, C{a, d, f}, then A × (B ∪ C) is:

Assume that P(A) = P(B) show that A = B.

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers.
Find the number of people who read exactly one newspaper.

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers.
Find the number of people who read at least one of the newspaper.

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only?

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The set D = {x : x is a prime number which is a divisor of 60} in roster form is {1, 2, 3, 4, 5}.
Reason: The set E = the set of all letters in the word ‘TRIGONOMETRY’, in the roster form is {T, R, I, G, O, N, M, E, Y}.

1. A is true, R is true; R is a correct explanation of A.
2. A is true, R is true; R is not a correct explanation of A.
3. A is true; R is false.
4. A is false; R is true.

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The set A = {x : x is an even prime number greater than 2} is the empty set.
Reason: The set B = {x : x² = 4, x is odd} is not an empty set.

1. A is true, R is true; R is a correct explanation of A.
2. A is true, R is true; R is not a correct explanation of A.
3. A is true; R is false.
4. A is false; R is true.

The school organised a farewell party for 100 students and school management decided three types of drinks will be distributed in farewell party ie. Milk (M), Coffee (C) and Tea (T). Organiser reported that 10 students had all the three drinks M, C, T. 20 students had M and C; 30 students had C and T; 25 students had M and T. 12 students.had M only; 5 students had C only; 8 students had T only.

Based on the above information, answer the following questions.

1. The number of students who did not take any drink, is

1. 20
2. 30
3. 10
4. 25

2. The number of students who prefer Milk is

1. 47
2. 45
3. 53
4. 50

3. The number of students who prefer Coffee is

1. 47
2. 53
3. 45
4. 50

4. The number of students who prefer Tea is

1. 51
2. 53
3. 50
4. 47

5. The number of students who prefer Milk and Coffee but not tea is

1. 12
2. 10
3. 15
4. 20

In a library, 25 students read physics, chemistry and mathematics books. It was found that 15 students read mathematics, 12 students read physics while 11 students read chemistry. 5 students read both mathematics and chemistry, 9 students read physics and mathematics. 4 students read physics and chemistry and 3 students read all three subject books.

Based on the above information, answer the following questions.

1. The number of students who reading only chemistry is:

1. 5
2. 4
3. 2
4. 1

2. The number of students who reading only mathematics is:

1. 4
2. 3
3. 5
4. 11

3. The number of students who reading only one of the subjects is:

1. 5
2. 11
3. 8
4. 6

4. The number of students who reading atleast one of the subject is:

1. 20
2. 22
3. 23
4. 21

5. The number of students who reading none of the subject is:

1. 2
2. 4
3. 3
4. 5

In a company, 100 employees offered to do a work. In out of them, 10 employees offered ground floor only, 15 employees offered first floor only, 10 employees offered second floor only, 30 employees offered second floor and ground floor to work, 25 employees offered first and second floor, 15 employees offered ground and first floor, 60 employees offered second floor.

Based on the above information answer the following questions.

1. The number of employees who offered all three floors.

1. 5
2. 3
3. 4
4. 6

2. The number of employees who offered ground floor.

1. 50
2. 60
3. 65
4. 70

3. The number of employees who offered first floor.

1. 40
2. 45
3. 50
4. 55

4. The number of employees who offered ground and first floor but not second floor.

1. 10
2. 15
3. 20
4. 25

5. The number of employees who did not offer any of the above three floors.

1. 15
2. 10
3. 5
4. 0

In an University, out of 100 students 15 students offered Mathematics only, 12 students offered Statistics only, 8 students offered only Physics, 40 students offered Physics and Mathematics, 20 students offered Physics and Statistics, 10 students offered Mathematics and Statistics, 65 students offered Physics.
Based on the above information answer the following questions.

1. The number of students who offered all the three subjects is:

1. 4
2. 3
3. 2
4. 5

2. The number of students who offered Mathematics is:

1. 62
2. 65
3. 55
4. 60

3. The number of students who offered statistics is:

1. 31
2. 35
3. 39
4. 34

4. The number of students who offered mathematics and statistics but not physics is:

1. 7
2. 6
3. 5
4. 4

5. The number of students who did not offer any of the above three subjects is:

1. 4
2. 1
3. 5
4. 3