Q.1 Which of the following is the universal set for natural numbers less than 6?
{1,2,3,4,5}
{0,1,2,3,4,5}
{1,2,3,4,5,6}
{0,1,2,3,4,5,6}
Explanation - Natural numbers start from 1, so natural numbers less than 6 are {1,2,3,4,5}.
Correct answer is: {1,2,3,4,5}
Q.2 If A = {2,4,6,8} and B = {4,8,12}, then A ∩ B equals?
{2,6}
{4,8}
{12}
∅
Explanation - Intersection contains elements common to both sets. Common elements are 4 and 8.
Correct answer is: {4,8}
Q.3 The empty set is denoted by:
{}
Ø
Both {} and Ø
0
Explanation - The empty set is usually denoted by {} or Ø. Symbol 0 refers to the number zero, not a set.
Correct answer is: Both {} and Ø
Q.4 If A = {a,b,c} then number of subsets of A is?
3
6
8
9
Explanation - Number of subsets of a set with n elements is 2^n. Here, n=3 so 2^3 = 8.
Correct answer is: 8
Q.5 Which of the following is a relation from A={1,2} to B={x,y}?
{(1,x), (2,y)}
{(x,1),(y,2)}
{1,2,x,y}
{(1,1),(2,2)}
Explanation - A relation from A to B is a subset of A×B. Only {(1,x),(2,y)} belongs to A×B.
Correct answer is: {(1,x), (2,y)}
Q.6 Which of these is always true for any set A?
A ⊆ A
A ∈ A
∅ ∈ A
A ⊂ ∅
Explanation - Every set is a subset of itself. The other statements are not always true.
Correct answer is: A ⊆ A
Q.7 If U = {1,2,3,4,5}, A = {1,3,5}, then A′ (complement of A) is:
{1,3,5}
{2,4}
{2,3,4}
{1,2,5}
Explanation - Complement is elements of U not in A. U - A = {2,4}.
Correct answer is: {2,4}
Q.8 Which is true about the empty set?
It is a subset of every set
It is equal to every set
It contains all elements
It has infinite elements
Explanation - By definition, the empty set is a subset of all sets, but not equal unless the set is also empty.
Correct answer is: It is a subset of every set
Q.9 If A = {1,2}, B = {2,3}, then A ∪ B equals?
{1,2}
{2,3}
{1,2,3}
{1,3}
Explanation - Union is all elements in A or B. So A ∪ B = {1,2,3}.
Correct answer is: {1,2,3}
Q.10 What is the power set of {a,b}?
{a,b}
{{a},{b}}
{{∅},{a},{b},{a,b}}
{{a,b}}
Explanation - Power set is the set of all subsets. For {a,b}, subsets are ∅,{a},{b},{a,b}.
Correct answer is: {{∅},{a},{b},{a,b}}
Q.11 The number of elements in P({1,2,3,4}) is:
4
8
12
16
Explanation - If a set has n elements, its power set has 2^n elements. For 4 elements, 2^4=16.
Correct answer is: 16
Q.12 Which of the following is not a subset of {1,2,3}?
∅
{1,2}
{4}
{1}
Explanation - Subset must contain elements from the original set. 4 is not in {1,2,3}.
Correct answer is: {4}
Q.13 If A={1,2,3}, B={3,4,5}, then A-B equals:
{1,2,3,4,5}
{3}
{1,2}
{4,5}
Explanation - A-B means elements in A but not in B. So {1,2}.
Correct answer is: {1,2}
Q.14 A relation R on a set A is symmetric if:
(a,b) ∈ R implies (b,a) ∈ R
(a,a) ∈ R
(a,b) ∈ R and (b,c) ∈ R implies (a,c) ∈ R
R contains ∅
Explanation - A symmetric relation requires that for every (a,b) in R, the pair (b,a) must also be in R.
Correct answer is: (a,b) ∈ R implies (b,a) ∈ R
Q.15 What is the Cartesian product A×B if A={1,2}, B={a}?
{(1,a),(2,a)}
{(a,1),(a,2)}
{1,2,a}
{(1,2),(a)}
Explanation - Cartesian product is all ordered pairs (a,b) where a ∈ A and b ∈ B.
Correct answer is: {(1,a),(2,a)}
Q.16 If R = {(1,1),(2,2),(3,3)} on A={1,2,3}, then R is:
Reflexive only
Symmetric only
Reflexive, symmetric, transitive
Not an equivalence relation
Explanation - This is the identity relation, which is reflexive, symmetric, and transitive, hence an equivalence relation.
Correct answer is: Reflexive, symmetric, transitive
Q.17 The number of subsets of a set with 5 elements is:
10
20
25
32
Explanation - Number of subsets = 2^n. For n=5, 2^5=32.
Correct answer is: 32
Q.18 If A={1,2,3}, then the relation R = {(1,2),(2,3)} is:
Reflexive
Symmetric
Transitive
None
Explanation - R does not contain (1,1),(2,2),(3,3) so not reflexive; not symmetric as (2,1) not in R; not transitive as (1,3) missing.
Correct answer is: None
Q.19 Which of the following sets is finite?
Set of natural numbers
Set of integers
Set of even numbers
Set of prime numbers less than 20
Explanation - All others are infinite. Prime numbers less than 20 are {2,3,5,7,11,13,17,19}.
Correct answer is: Set of prime numbers less than 20
Q.20 If A={a,b}, B={1,2}, then number of elements in A×B is:
2
4
6
8
Explanation - Cartesian product has |A|×|B| elements. Here 2×2=4.
Correct answer is: 4
Q.21 If A={1,2,3}, what is A×A?
{(1,1),(2,2),(3,3)}
{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)}
{(1,2),(2,3)}
{(1,3)}
Explanation - Cartesian product A×A has ordered pairs of all elements in A with A.
Correct answer is: {(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)}
Q.22 If R = {(a,b) | a,b ∈ N and a divides b}, then R is:
Reflexive
Symmetric
Transitive
Reflexive and transitive
Explanation - Every number divides itself (reflexive). If a divides b and b divides c, then a divides c (transitive). Not symmetric.
Correct answer is: Reflexive and transitive
Q.23 Which of the following represents an equivalence relation?
R on Z defined by aRb if a-b is even
R on Z defined by aRb if a<b
R on N defined by aRb if a divides b
R on R defined by aRb if a ≤ b
Explanation - Difference being even is reflexive, symmetric, and transitive, hence equivalence relation.
Correct answer is: R on Z defined by aRb if a-b is even
Q.24 If A={x | x is a letter in the word 'MATH'}, then n(A) is:
3
4
5
6
Explanation - The word MATH has 4 distinct letters {M,A,T,H}. So n(A)=4.
Correct answer is: 4
Q.25 If A and B are disjoint sets, then A ∩ B equals:
A
B
∅
A∪B
Explanation - Disjoint sets have no common elements, so their intersection is ∅.
Correct answer is: ∅