FSc Part 1 Maths chapter 2: Sets, functions and groups MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

27 exam-style questions on Sets, functions and groups, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

27 questions · 3 topics · 10 per test

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What chapter 2 covers

Ten Sets, functions and groups questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. Which statement about the empty set ∅ is correct?

  1. A
    ∅ is a proper subset of every set
  2. B
    ∅ is a subset of every set
  3. C
    ∅ is an element of every set
  4. D
    ∅ = {0}
Show answer

Answer: B. ∅ is a subset of every set, but it is not a proper subset of itself. {0} is not empty: it has the element 0.

2. Which set-builder form describes the set {2, 4, 6, 8, ...}?

  1. A
    {x | x ∈ N ∧ x is even}
  2. B
    {x | x ∈ Z ∧ x is even}
  3. C
    {x | x ∈ W ∧ x is even}
  4. D
    {x | x ∈ N ∧ x < 10}
Show answer

Answer: A. The set starts at 2 and has no negatives. Even integers would include 0 and negatives, and even whole numbers would include 0.

3. The conditional p → q is false only when

  1. A
    p and q are both true
  2. B
    p is false and q is true
  3. C
    p and q are both false
  4. D
    p is true and q is false
Show answer

Answer: D. A true hypothesis cannot lead to a false conclusion. In every other case p → q is true, including when p is false.

4. A set A has 4 elements. The number of elements in its power set P(A) is

  1. A
    16
  2. B
    8
  3. C
    4
  4. D
    24
Show answer

Answer: A. A set with n elements has 2n subsets, so P(A) has 24 = 16 elements.

5. The operation a * b = a − b on the set of integers is

  1. A
    associative but not commutative
  2. B
    commutative and associative
  3. C
    commutative but not associative
  4. D
    neither commutative nor associative
Show answer

Answer: D. 1 − 2 ≠ 2 − 1, so it is not commutative. (1 − 2) − 3 = −4 but 1 − (2 − 3) = 2, so it is not associative.

6. If f(x) = 2x + 3, then f−1(x) is

  1. A
    (x + 3)/2
  2. B
    (x − 3)/2
  3. C
    1/(2x + 3)
  4. D
    2x − 3
Show answer

Answer: B. Put y = 2x + 3 and solve for x: x = (y − 3)/2. The inverse function is not the reciprocal 1/f(x).

7. By De Morgan's law, (A ∪ B)′ is equal to

  1. A
    A ∩ B′
  2. B
    A′ ∪ B′
  3. C
    A′ ∩ B′
  4. D
    (A ∩ B)′
Show answer

Answer: C. The complement of a union is the intersection of the complements. A′ ∪ B′ is the complement of A ∩ B.

8. The identity element of the set of real numbers under multiplication is

  1. A
    0
  2. B
    1
  3. C
    −1
  4. D
    there is no identity element
Show answer

Answer: B. a × 1 = 1 × a = a for every real a. 0 is the identity for addition, not multiplication.

9. The set {1, −1, i, −i} under multiplication is

  1. A
    closed but without an identity element
  2. B
    a group that is not abelian
  3. C
    not closed
  4. D
    an abelian group
Show answer

Answer: D. All products stay in the set, 1 is the identity, the inverses are 1, −1, −i, i, and multiplication of complex numbers is commutative.

10. Which of the following sets is infinite?

  1. A
    the set of letters in the word MATHEMATICS
  2. B
    the set of days of the week
  3. C
    {x | x ∈ N ∧ x < 1000}
  4. D
    the set of rational numbers between 0 and 1
Show answer

Answer: D. Between any two rational numbers there is another, so there are infinitely many between 0 and 1. The other sets can be counted to an end.

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Ways to practise this chapter

Sets, functions and groups: questions students ask

How many Sets, functions and groups MCQs are there?

27, each with the answer and a short explanation, across 3 topics: Sets and set operations, Logic, relations and functions, Binary operations and groups. Every chapter test draws ten of them, so you can take it many times.

Is the FSc Part 1 Maths chapter 2 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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