GATE | GATE MOCK 2017 | Question 27

Consider the Following regular expressions

              
r1 = 1(0 + 1)*
r2 = 1(1 + 0)+
r3 = 11*0

What is the relation between the languages generated by the regular expressions above ?

(A) L (r1) ⊆ L (r2) and L(r1) ⊆ L(r3)
(B) L (r1) ⊇ L (r2) and L(r2) ⊇ L(r3)
(C) L (r1) ⊇ L (r2) and L(r2) ⊆ L(r3)
(D) L (r1) ⊇ L (r3) and L(r2) ⊆ L(r1)

Answer: (B)

Explanation:
Clearly r1 is a superset of both r2 and r3 as string 1 can not be generated by r2 and r3. r2 is a superset of r3 as string 11 is not present in L(r3) but in L(r2).


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