Regular expression for the language L = { w ∈ {0, 1}* | w has no pair of consecutive zeros} is

Question

A.    (1 + 010)*
B.    (01 + 10)*
C.    (1 + 010)* (0 + λ)
D.    (1 + 01)* (0 + λ)

Answer 1

Correct answer would be D) (1 + 01)* (0 + λ) 

Strings 010010 can be generated with option (a) by using 010 twice.

String 1001 can be generated with option (b).

string 0100 can be generated with option (c).

So except d) option all can generate strings with 00 as a substring.

Answer 2

Answer D)

The Language here is L={⋋,0,1,01,011,101,0101..................}

But

for A) 010010 possible

B)1001 possible

C)0100 possible

These all violates the condition for no pair of consecutive 0

Comments

What about (1 + 01)*  ?

---

In that case all strings will end with 1 but it can also end with 0 so including (0+ null) Is necessary