UGC NET CSE | June 2016 | Part 3 | Question: 22

Question

The symmetric differences of two sets $S_1$ and $S_2$ is defined as:

$S_1 \oplus S_2 =\{x \mid x \in S_1 \text{ or } x \in S_2, \text{ but x is not in both } S_1 \text{ and } S_2 \}$

The nor of two languages is defined as

$nor(L_1, L_2)=\{w \mid w \notin L_1 \text{ and } w \notin L_2 \}$

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 1

S1⊕S2= $S1^c$S2 + S1$S2^c$

regular languages are closed under intersection,complementation and union  and hence they are closed under set difference

nor(L1+L2)= $L1^c$.$L2^c$  (from demorgan's law)

here . represents intersection

regular languages are closed under complementation and intersection and hence they are closed under nor.

option c)