# UGC-NET | UGC NET CS 2016 July – III | Question 22

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}}

The nor of two languages is defined as

nor (L_{1}, L_{2}) = {w|w |∈L_{1} and w |∈ L_{1}}.

Which of the following is correct?**(A)** The family of regular languages is closed under symmetric difference but not closed under nor.**(B)** The family of regular languages is closed under nor but not closed under symmetric difference.**(C)** The family of regular languages are closed under both symmetric difference and nor.**(D)** The family of regular languages are not closed under both symmetric difference and nor.**Answer:** **(C)****Explanation:**

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