# Cross Product Method over DFAs

We will try to understand this property using one example.

So as you see in the above picture, we have taken two DFAs

- Even no of a's
- Even no of b's

- L1 = {ε, baa, aa, aba, aab, aaaa, ... }
- L2 = {ε bb, abb, bab, bba, ...}

After taking cross product we will find the below DFA, already we have seen this DFA in previous exampels

As, L = {ab, aab, abb, aaab, ...}

#### How we have designed:

{A, B} X {C, D} = {AC, AD, BC, BD}

We should know the transition of the above four states

**Note: clearly the language is infinite**

*You can also take some examples from the previous exercises for practice.*