Peter Linz Edition 4 Exercise 4.3 Question 23 (Page No. 124)

Question

Is the family of regular languages closed under infinite intersection?

Answer 1

Regular Language Are Closed Under Infinite Intersection Of Regular Language.( i think correct me if i am wrong)

 

Regular Language Are " NOT "  Closed Under Infinite Union Of Regular Language.

L1 = {ab}

L2 = {a2b2}

L3 = {a3b3}

.

.

.

Union(L1, L2, L3.................) = { anbn | n>1 }

Answer 2

No , the family of regular languages are not closed under infinite intersection.

https://gateoverflow.in/3078/proof-regarding-infinite-union-intesection