Vaidikalaya

MCQ On Set Cardinality

Q1. The cardinality of the set A = {1, 2, 3, 4, 6} is?.
  1. 5
  2. 6
  3. Integer
  4. None of the mentioned

Answer: a, 5

Q2. For two equal sets there ___________.
  1. Cardinality is same
  2. Cardinality is different
  3. May be same or different
  4. None of the mentioned

Answer: a, Cardinality is same

Q3. If A is a subset of B then _______.
  1. The cardinality of A is greater than B
  2. The cardinality of B is greater than A
  3. Can’t say
  4. None of the mentioned

Answer: b, The cardinality of B is greater than A

Solution: B contains all the elements of A, as well as other elements.

Q4. If there is a bijection between two sets A and B then _______.
  1. Cardinality of A is greater than B
  2. Cardinality of B is greater than A
  3. Cardinality of B is equal to A
  4. None of the mentioned

Answer: c, Cardinality of B is equal to A

Solution: If there is bijection then two sets A and B will have same cardinality.

Q5. Cardinality of the set of even prime number under 10 is 4..
  1. TRUE
  2. FALSE

Answer: b, FALSE

Solution: Since 2 is only even prime thus cardinality should be 1.

Q6. What is the cardinality of the power set of the set {0,1,2}?.
  1. 6
  2. 7
  3. 8
  4. 9

Answer: c, 8

Solution:

The cardinality of the power set of a set with n elements is: 2n

Q7. The cardinality of the empty set ∅ is.
  1. 1
  2. 0
  3. -1
  4. Undefined

Answer: b, 0

Solution: Empty set has no elements.

Q8. If |A| = 10, |B| = 15 and |A ∩ B| = 5, then |A ∪ B| is.
  1. 30
  2. 20
  3. 25
  4. 15

Answer: b, 20

Solution: ∣A∪B∣=∣A∣+∣B∣−∣A∩B∣

Q9. If A and B are disjoint sets and |A| = 7, |B| = 9, then |A ∪ B| is.
  1. 2
  2. 9
  3. 7
  4. 16

Answer: d, 16

Solution: Disjoint ⇒ A ∩ B = ∅

Q10. If |A| = 4, then the cardinality of the power set P(A) is.
  1. 8
  2. 12
  3. 16
  4. 4

Answer: c, 16

Solution:

∣P(A)∣=2∣A∣ =24 =16

Q11. If A ⊆ B and |A| = |B|, then.
  1. A ⊂ B
  2. A ≠ B
  3. A = B
  4. A = ∅

Answer: c, A = B

Solution: If subset and same cardinality ⇒ equal sets.

Q12. If |A ∩ B| = |A|, then.
  1. A ⊆ B
  2. B ⊆ A
  3. A = ∅
  4. A ∪ B = B

Answer: a, A ⊆ B

Solution: All elements of A are present in B.

Q13. In a survey of 60 people, 25 liked tea, 30 liked coffee, and 10 liked both. How many people liked only tea?.
  1. 35
  2. 45
  3. 15
  4. 25

Answer: c, 15

Solution:

People who like Tea (T) = 25
People who like Coffee (C) = 30
People who like both (T ∩ C) = 10
Only Tea=∣T∣−∣T∩C∣ = 25−10 = 15

Q14. In a class of 40 students, 22 play hockey, 26 play basketball, and 14 play both. How many students do not play either of the games?.

Question Image

  1. 12
  2. 6
  3. 14
  4. 10

Answer: b, 6

Solution:

Total students = 40
n(H)=22
n(B) = 26
n(H ∩ B) = 14
n(H ∪ B) = n(H) + n(B) - n(H ∩ B) = 22 + 26 - 14 = 34.
Students not playing neither = Total students - n(H ∪ B) = 40 - 34 = 6.
6 students do not play either hockey or basketball

Q15. A class has 60 students. 35 students play football, 40 play cricket, and 15 play both. How many students play only one sport?.
  1. 60
  2. 45
  3. 20
  4. 30

Answer: b, 45

Solution:

Total students = 60
Football (F) = 35
Cricket (C) = 40
Both (F ∩ C) = 15

Students who play only football
Only Football = ∣F∣−∣F∩C∣ = 35−15 = 20
Students who play only cricket
Only Cricket = ∣C∣−∣F∩C∣ = 40−15 = 25
Students who play only one sport = 20+25 = 45