Question

Asked Mar 29, 2019

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The *symmetric difference* of two sets *S*_{1} and *S*_{2} is defined as

*S*_{1} ⊝ *S*_{2} = {*x* : *x* ∈ *S*_{1} or *x* ∈ *S*_{2}, but *x* is not in both *S*_{1} and *S*_{2}}.

Show that the family of regular languages is closed under symmetric difference.

Step 1

**Solution:**

Given that,

The symmetric difference between two sets such as “S_{1}” and “S_{2}” can be expressed in terms of regular set operations.

We know that the symmetric difference of “S_{1}” and “S_{2}” is defined as,

Step 2

Since we have for any set A and B:

Step 3

So, we can define symmetric dif...

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