UGC NET CSE | January 2017 | Part 3 | Question: 21

Question

Given the following statements:

1. A class of languages that is closed under union and complementation has to be closed under intersection
2. A class of languages that is closed under union and intersection has to be closed under complementation

Which of the following options is correct?

• A. Both (i) and (ii) are  false
• B. Both (i) and (ii) are true
• C. (i) is true, (ii) is false
• D. (i) is false, (ii) is true

Comments

A intersection  B  = (A'UB')'  . since set is closed under complement and union   so it must be closed  under intersection  so a is true  ( union and complement-> intersection

no such relation between union , intersection  --> complementation

Answer 1

FIRST STATEMENT IS TRUE

REGULER,CSL,RECURSIVE  CLOSED UNDER UNION AND COMPLEMENTATION  AND THESE ARE  ALSO CLOSED UNDER INTERSECTION

SECOND STATEMENT IS FALSE

RE  CLOSED UNDER UNION AND INTERSECTION HAS  BUT NOT CLOSED UNDER COMPLEMENTATION

 

Answer 2

Option C) is correct.

Answer 3

L1 $\cup$ ~(L2) = L1 $\cap$ L2

here we can tell about intersection using union and complementation. but we can’t tell about complementation using union and intersection.

hence C is correct option.