Download Careers360 App
NIRF Engineering Ranking 2025: Complete List of Top Colleges

Union of sets, Properties of union - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Union of sets, Properties of union is considered one of the most asked concept.

  • 41 Questions around this concept.

Solve by difficulty

If  X=\left \{ 4^{n}-3n-1\; :\; n\; \epsilon \; N \right \}\; and\;\; Y= \; \left \{9(n-1):n\; \epsilon \; N \right \},where\; N is a set of natural numbers, then  X\cup Y  is equal equal to :

$(A \cup B) \cup C=A \cup(B \cup C)$ is called:

$A-(B \cup C)=$

$A \cup \phi=$

$A \cup A=$

$U \cup A=$

$A \cup A^{\prime}=$

GNA University B.Tech Admissions 2025

100% Placement Assistance | Avail Merit Scholarships | Highest CTC 43 LPA

UPES B.Tech Admissions 2025

Ranked #42 among Engineering colleges in India by NIRF | Highest Package 1.3 CR , 100% Placements | Last Date to Apply: 30th July | Limited seats available in select program

If $\mathrm{A}=\{2,3,5\}$ and $\mathrm{B}=\{\mathrm{x}: \mathrm{x} \in \mathrm{N}$ and $\mathrm{x}<5\}$ Then $A \cup B=$

What is the commutative property of union?

JEE Main 2026: Preparation Tips & Study Plan
Download the JEE Main 2026 Preparation Tips PDF to boost your exam strategy. Get expert insights on managing study material, focusing on key topics and high-weightage chapters.
Download EBook

Which of the following is a commutative binary operation on R ?

Concepts Covered - 1

Union of sets, Properties of union

Venn Diagram

A diagram that represents or shows different sets is called a Venn diagram.

The universal set (U) is usually represented by a rectangle and its subsets are usually represented by circles (or any other closed curve).

For example, the set of natural numbers (N) is a subset of the set of whole numbers (W), which is a subset of integers (here, integer (Z) is the universal set). 

Example

In the above figure Universal Set $(U)=\{0,1,2,3,4,5,6,7,8\}$
Set $A=\{2,3,5,7,8,9,10\}$ and $B=\{2,3,5\}$
$A$ is a subset of $U(A \subset U)$
$B$ is a subset of $A(B \subset A)$
 

Union of Sets
Let $A$ and $B$ be any two sets. The union of $A$ and $B$ is the set which consists of all the elements of $A$ and all the elements of B, the common elements being taken only once. The symbol ' $u$ ' is used to denote the union.

Symbolically, we write $A \cup B=\{x: x \in A$ or $x \in B\}$.


Properties of Union

$A \cup B=B \cup A \quad$ (Commutative Property)
$(A \cup B) \cup C=A \cup(B \cup C)$ (Associative property)
$\mathrm{A} \cup \varphi=\mathrm{A}$ (Law of identity element, $\varphi$ is the identity of Null Set)
$\mathrm{A} \cup \mathrm{A}=\mathrm{A}$ (Idempotent law)
$U \cup A=U($ Law of $U)$
If $A$ is a subset of $B$, then $A \cup B=B$

Study it with Videos

Union of sets, Properties of union

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Books

Reference Books

Union of sets, Properties of union

Mathematics Textbook for Class VII

Page No. : 13

Line : 30

E-books & Sample Papers

Get Answer to all your questions

Back to top