# The string 1101 does not belong to the set represented by:

| The string 1101 does not belong to the set represented by:

A. (00 + (11)*0)

B. 1(0 + 1)*101

C. (10)* (00 + 11)* (01)*

D. 110*(0 + 1)

#### SOLUTION

Option 1: (00 + (11)*0)

This regular expression generates the strings like:

{0, 00, 000, 110, 11011, 11110, 11000, …} .

It is not generating 1101 because after every 11 there is a single 0 possible but a single 1 is not possible in any case.

Option 2: 1(0 + 1)*101

It is generating strings of type: {1101, 10101, 11101, 101101, ………}.

It contains the string 1101, so not the correct answer.

Option 3: (10)* (00 + 11)* (01)*

This regular expression is generating strings of type: {ϵ, 10, 00, 11, 01, 1000, 1011, 1001, 1101…….}.

It is possible to get 1101 in this expression. So, it is the not correct answer.

Option 4: 110*(0 + 1)

In this, set of strings that are possible are: {110, 111, 1100, 1101, 11001,……..}.

So it is generating the string 1101. So, it is not the correct answer.