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

$A\cup B=B\cup A$ (Commutative Property)
$(A\cup B)\cup C=A\cup (B\cup C)$ (Associative property)
$\mathrm{A}\cup \phi =\mathrm{A}$ (Law of identity element, $\phi$ 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 $A\cup B=B$