Q20,paper2,J1 3 . Given L1=L(a*baa*) and L2=L(ab*). The regular expression corresponding to language L3 = L1/L2 (right quotient) is given by

(A) a*b

(B) a*baa*

(C) a*ba*

(D) None of the above 
Answer c.

Explanation.

L1. Of word length 1{}

L1 of word length 2{ba}

L1 of word length3.{aba,baa}.

L1 of word length4{abaa,aaba,baaa}.

L2 of word length 1{a}.

L2 of word length2{ab}.

L2 of word length 3{abb}.

L2 of word length 4{abbb}.

Right  quotient is

Let  L1 is the language {fish,dog,carrot} and that L2 is the language {rot}. Then L1/L2, the quotient of L1 by L2, is the language {car}, because car is the only string for which you can append something from L2 to get something from L1.

L1/L2={ba,,aba,baa,abaa,aaba,baaa}.

Hence option C.