Question

Justify your answer to each of the following true/false statements:

l. Every subset of a regular set is regular

2. The intersection of a regular set with a finite set is regular

3. The union of a regular set with an infinite set is regular

4. The positive closure of a regular set is regular

Answer 1

1.answer)FALSE

counter example: L=set of all string over a,b

regular expression=(a+b)^*

take subset L2=equal number of a's follwed by equal number of b's

L2 's returlar expression is {aⁿbⁿ /n>=1}.

L2 is not regurlar language.so answer is FALSE.

2.TRUE

Finite set means it is always regualar.insesection of a regular set with finite set is always regular.

3.TRUE

union of regular set with infinite set is always regular

4.TRUE

if r1 is regular language then its closure is also regular