let r1=(a+bb)* , r2=(a*+b* ), r3=(aa+b)* which 0f the following is true?

Question

A)L(r1)⊆L(r2) and L(r3)⊆L(r2)

b) L(r2)⊆L(r1)  and L(r2)⊆L(r3)

C) L(r1)=L(r3)⊆L(r2)

D) L(r1)⋃L(r3)=L(r2)

plz explain with explanation

Answer 1

plz correct me.....

Comments

I agree with the solution and the last part

L(r2) ⊆ L(r1) U L(r3)

Because language produced by r2 is Either only streams of a's or only streams of b's but not both.

Moreover, both L(r1) and L(r3) when mixed together(Union) can handle cases of when we have only streams of a's or streams of b's which is the language generated by L(r2)