SETS
Test your knowledge of sets! This quiz covers the basics of set theory including types of sets, set notation, Venn diagrams, union, intersection, and complements. Ideal for students revising foundational mathematics.
1 / 40
Which of the following is a singleton set?
A singleton set has exactly one element.
2 / 40
The power set of {1, 2} is:
The power set includes all possible subsets.
3 / 40
The complement of set A = {1, 2} in the universal set U = {1, 2, 3, 4} is:
The complement consists of elements in U but not in A.
4 / 40
Which of the following is an empty set?
No real number satisfies x² = -1.
5 / 40
If A = {a, b} and B = {a, b, c}, then A is a:
A ⊆ B but A ≠ B.
6 / 40
The Cartesian product A × B where A = {1} and B = {2, 3} is:
A × B pairs each element of A with each in B.
7 / 40
If A = {x | x is an even number}, then A is:
There are infinitely many even numbers.
8 / 40
Two sets A and B are equal if:
Both sets must have identical elements.
9 / 40
The number of subsets of {a, b, c} is:
A set with n elements has 2^n subsets.
10 / 40
The universal set is:
It contains all objects under consideration.
11 / 40
If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B is:
Union includes all distinct elements from both sets.
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If A = {1, 2} and B = {2, 3}, then A ∩ B is:
Intersection includes only common elements.
13 / 40
The difference A − B where A = {1, 2, 3} and B = {2, 4} is:
Elements in A but not in B.
14 / 40
If A = {a, b} and B = {b, c}, then A × B contains:
Cartesian product pairs all elements.
15 / 40
The symmetric difference A Δ B (elements in A or B but not both) for A = {1, 2} and B = {2, 3} is:
Symmetric difference excludes common elements.
16 / 40
If A ⊆ B, then A ∪ B is:
Since A is a subset, the union is B.
17 / 40
If A = {1, 2, 3} and B = {4, 5}, then A ∩ B is:
Disjoint sets have no common elements.
18 / 40
The number of elements in A × B where A = {1, 2} and B = {a, b, c} is:
|A × B| = |A| × |B| = 2 × 3 = 6.
19 / 40
(A ∪ B) − (A ∩ B) for A = {1, 2} and B = {2, 3} is:
This is the symmetric difference.
20 / 40
The complement of the universal set U is:
No elements lie outside U.
21 / 40
Which of the following is an irrational number?
π cannot be expressed as a fraction.
22 / 40
The set {1, 2, 3, …} represents:
Counting numbers starting from 1.
23 / 40
Which of the following is a rational number?
It can be written as 3/4.
24 / 40
The recurring decimal 0.3̄ is equal to:
0.3̄ = 1/3.
25 / 40
The interval notation (2, 5] represents:
Parenthesis excludes 2, bracket includes 5.
26 / 40
The union of rational and irrational numbers forms:
All real numbers are either rational or irrational.
27 / 40
The intersection of ℤ (integers) and ℚ (rationals) is:
All integers are rational numbers.
28 / 40
The set {…, -2, -1, 0, 1, 2, …} is:
Includes negatives, zero, and positives.
29 / 40
The number 0 belongs to:
0 is in both sets.
30 / 40
The interval [1, 4) ∩ (2, 5] is:
Overlap between the two intervals.
31 / 40
A binary operation is:
Binary operations map S × S → S.
32 / 40
The operation ∗ defined by a ∗ b = a + b – ab is:
Check a ∗ b = b ∗ a and (a ∗ b) ∗ c = a ∗ (b ∗ c).
33 / 40
Which property holds for subtraction (-) over integers?
a – b ≠ b – a, and (a – b) – c ≠ a – (b – c).
34 / 40
The identity element for addition on real numbers is:
a + 0 = a for any real a.
35 / 40
If ∗ is defined by a ∗ b = a² + b², then 2 ∗ 3 is:
2² + 3² = 4 + 9 = 13.
36 / 40
A binary operation is associative if:
Associativity requires grouping invariance.
37 / 40
The inverse of 5 under addition is:
5 + (-5) = 0 (the additive identity).
38 / 40
Which operation is distributive over addition?
a × (b + c) = (a × b) + (a × c).
39 / 40
If a∗b=a+b2, then 4∗6 is:
4+62=5
40 / 40
A binary operation is commutative if:
Commutativity means order does not matter.
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