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

Venn Diagram

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

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 ⊂ U)

B is a subset of A (B ⊂ 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 ‘∪’ is used to denote the union.

Symbolically, we write A U B = {x: x ∈ A or x ∈ B}.

Properties of union

• A ∪ B = B ∪ A        (Commutative Property)

• ( A B ) C = A ( B C)  (Associative property)

• A φ = A (Law of identity element, φ is the identity of Null Set)

• A A = A (Idempotent law)

• U A = U (Law of U)

• If A is a subset of B, then A ∪ B = B