Regular expression - Theory of Computing

Regular expression – Theory of Computing

Question 1 UGC NET June-2020
Consider the following regular expressions:
a) r=a(b+a)*
b) s=a(a+b)*
c) t=aa*b
Choose the correct answer from the options given below based on the relation between the languages generated by the regular expressions above:

A – L(r) ⊆ L(s) ⊆ L(t)

B – L(r) ⊇ L(s) ⊇ L(t)

C – L(r) ⊇ L(t) ⊇ L(s)

D – L(s) ⊇ L(t) ⊇ L(r)

Show Answer With Best Explanation

Answer- B
Explanation:
R = {a, ab, aa, aba, aaa, aab, abb…….}
S = {a, aa, ab, aab, aaa, abb, aba…….}
T = {ab, aab, aaab, …………………………}
If you notice then r ⊇ s ⊇ t