The symmetric difference of two sets S1 and S2 is defined asS1 ⊝ S2 = {x : x ∈ S1 or x ∈ S2, but x is not in both S1 and S2}.Show that the family of regular languages is closed under symmetric difference.

Question
Asked Mar 29, 2019
39 views

The symmetric difference of two sets S1 and S2 is defined as

S1 ⊝ S2 = {x : x ∈ S1 or x ∈ S2, but x is not in both S1 and S2}.

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

check_circle

Step 1

Solution:

Given that,

The symmetric difference between two sets such as “S1” and “S2” can be expressed in terms of regular set operations.

We know that the symmetric difference of “S1” and “S2” is defined as,

Step 2

Since we have for any set A and B:

Step 3

So, we can define symmetric dif...

Want to see the full answer?

See Solution

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in