Union process in DFA

Let’s understand the Union process in Deterministic Finite Automata (DFA) with the help of below example.

Designing a DFA for the set of string over {a, b} such that string of the language start and end with different symbols. There two desired language will be formed:

L1 = {ab, aab, aabab, .......}
L2 = {ba, bba, bbaba, .......} 

L₁= {starts with a and ends with b } and L₂= {starts with b and ends with a}.
Then L= L₁ ∪ L₂ or L=L₁ + L₂

State Transition Diagram for the language L₁:

This DFA accepts all the string starting with a and ending with b. Here, State A is initial state and state C is final state.

State Transition Diagram for the language L₂:

This DFA accepts all the string starting with b and ending with a. Here, State A is initial state and state C is final state.

Now, Taking the union of L₁ and L₂ language which gives the final result of the language which starts and end with different elements.
State Transition Diagram of L₁ ∪ L₂:

Thus as we see that L₁ and L₂ have been combined through union process and this final DFA accept all the language containing strings starting and ending with a different symbols.
Note: From above example we can also infer that regular languages are closed under union(i.e Union of two regular languages is also regular).