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

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 $(U)=\{0,1,2,3,4,5,6,7,8,9,10\}$
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 $A \cup B=B$