GATE - TOC Regular Languages & FA

Question

Let L(r1)=(b*ab*ab*ab*)* & L(r2)=(b*ab*ab*)*. What is L(r1) Intersection L(r2)?

a) (b*ab*ab*ab*)*

b) (b*ab*ab*)*

c) (b*ab*ab*)^6

d) (b*ab*ab*ab*ab*ab*ab*)*

Please do explain also.

Answer 1

Option d

L1 gives a is multiple 3 . And any number of b's.

L1= {aaa,aaaaaa,aaaaaaaaa....}

L2 gives a is multiple of 2

L2={aa,aaaa,aaaaaa.......}

L1 intersection L2= { a^6,a^12.....} ----> multiple of 6

Comments

Why is this so??