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We know, here R subset L so by formula R intersection L= R, but for any string R=L( both language are same) R intersection L can be R or L?

Correct me!
L and R are both languages ( set of strings) not a single string. In fact L is set of all possible strings over a,b and R is definitely a subset of L. There may be many common strings and intersection of both languages is R only bcoz its a proper subset.
Any anti-examplewhich is in L but not in R. Arent they same languages?
aabbbaaaabbb this is not in R. So pattern in R is a encloses b or not present at all but can not be present in interleaved manner.
Thanks bro got it!

+1 vote

It is same thing what we do in Set Theory,

Universe U={1,2,3,4,..,8,9,10}

A={1,2,3}

U ∩ A = A                      {Always.}

Now Relate L with U that is Simply the Universal Language And R is one of the Subsets of it.

So,L ∩ R will always be R here in this case.

In this given question there are some string possible in "L" which are not possible in "R" example string "abab" but all string possible in "R" is possible in "L". So here .."L intersection R"  is "R" for sure.