Sets in Algebra MCQs

By: Prof. Dr. Fazal Rehman Shamil | Last updated: January 31, 2025

\[
\textbf{MCQs on Sets with Answers}
\]

\[
\textbf{Q1: Which of the following represents the union of sets A and B?}
\]
\[
\text{(A) } A \cap B \quad \text{(B) } A – B \quad \text{(C) } A \cup B \quad \text{(D) } A \subseteq B
\]
\[
\textbf{Answer: (C) } A \cup B
\]

\[
\textbf{Q2: If A = \{1, 2, 3\} and B = \{3, 4, 5\}, what is A ∩ B?}
\]
\[
\text{(A) } \{1, 2, 3, 4, 5\} \quad \text{(B) } \{3\} \quad \text{(C) } \{1, 2\} \quad \text{(D) } \{4, 5\}
\]
\[
\textbf{Answer: (B) } \{3\}
\]

\[
\textbf{Q3: Which of the following is the complement of set A if universal set U = \{1, 2, 3, 4, 5\} and A = \{1, 2, 3\}?}
\]
\[
\text{(A) } \{1, 2, 3\} \quad \text{(B) } \{4, 5\} \quad \text{(C) } \{3, 4, 5\} \quad \text{(D) } \{2, 3, 4\}
\]
\[
\textbf{Answer: (B) } \{4, 5\}
\]

\[
\textbf{Q4: The power set of a set A is the set of all:}
\]
\[
\text{(A) } Proper subsets of A \quad \text{(B) } Subsets of A \quad \text{(C) } Elements of A \quad \text{(D) } Super sets of A
\]
\[
\textbf{Answer: (B) } Subsets of A
\]

\[
\textbf{Q5: If A = \{x | x \text{ is an even number}\} and B = \{x | x \text{ is a prime number}\}, what is A ∩ B?}
\]
\[
\text{(A) } \{2\} \quad \text{(B) } \{4, 6, 8\} \quad \text{(C) } \{1, 2, 3\} \quad \text{(D) } \{2, 3, 5\}
\]
\[
\textbf{Answer: (A) } \{2\}
\]

\[
\textbf{Q6: Which of the following sets is a subset of every set?}
\]
\[
\text{(A) } The empty set \quad \text{(B) } The universal set \quad \text{(C) } The set of all real numbers \quad \text{(D) } The set of all integers
\]
\[
\textbf{Answer: (A) } The empty set
\]

\[
\textbf{Q7: If A = \{1, 2, 3\} and B = \{3, 4, 5\}, what is A – B?}
\]
\[
\text{(A) } \{1, 2\} \quad \text{(B) } \{3\} \quad \text{(C) } \{4, 5\} \quad \text{(D) } \{1, 2, 3, 4, 5\}
\]
\[
\textbf{Answer: (A) } \{1, 2\}
\]

\[
\textbf{Q8: The Cartesian product of sets A = \{1, 2\} and B = \{x, y\} is:}
\]
\[
\text{(A) } \{(1, x), (1, y), (2, x), (2, y)\} \quad \text{(B) } \{(x, 1), (y, 2)\} \quad \text{(C) } \{1, 2, x, y\} \quad \text{(D) } \{(1, y), (2, x)\}
\]
\[
\textbf{Answer: (A) } \{(1, x), (1, y), (2, x), (2, y)\}
\]

\[
\textbf{Q9: If A = \{a, b, c\} and B = \{a, c, d\}, what is A ∪ B?}
\]
\[
\text{(A) } \{a, b, c\} \quad \text{(B) } \{a, b, c, d\} \quad \text{(C) } \{a, b, c, d, e\} \quad \text{(D) } \{b, c, d\}
\]
\[
\textbf{Answer: (B) } \{a, b, c, d\}
\]

\[
\textbf{Q10: Which of the following operations can be performed on two sets?}
\]
\[
\text{(A) } Intersection \quad \text{(B) } Union \quad \text{(C) } Difference \quad \text{(D) } All of the above
\]
\[
\textbf{Answer: (D) } All of the above
\]

More MCQs on Algebra (Collected from Past Papers)

1. Elementary Algebra – MCQs
2. Algebraic Expressions – MCQs
3. Algebraic Identities – MCQs
4. Commutative Algebra – MCQs
5. Linear Equations – MCQs
6. Graphing Linear Equations – MCQs
7. Inequalities in Algebra – MCQs
8. Absolute Value Inequalities – MCQs
9. Exponent – MCQs
10. Exponential Functions – MCQs
11. Logarithms – MCQs
12. Polynomials – MCQs
13. Factoring Methods – MCQs
14. Polynomial Arithmetic – MCQs
15. Quadratic Equation – MCQs
16. Linear Algebra – MCQs
17. Matrices in Algebra – MCQs
18. Functions in Algebra – MCQs
19. Sequences in Algebra – MCQs
20. Arithmetic in Algebra – MCQs
21. Combining Like Terms in Algebra – MCQs
22. Abstract Algebra – MCQs
23. Sets in Algebra – MCQs
24. Algebra Calculator – MCQs