regular Language

Question

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

L(r1)=starting with '1'.

L(r1)={1,10,11,101,1010,..........}

L(r2)=starting with 11 or 10.

L(r2)={11,10,1101,1010,101,.......}

L(r3)=starting with 1 and ends with 0.

L(r3)={10,110,1110,......}

we can conclude from above three

$L(r1)\supseteq L(r2) and L(r2)\supseteq L(r3)$