THEORY OF COMPUTATION

Question

Let $L_1= (0+1)^* , L_2=(01^*0 +1^*) \text{ and  } L3=(01^+0 +1^+ + \epsilon) $.

If $L=L_1 \cap  L_2 \cap  L_3$

Then find the number of strings in $L$ which do not contain $11$.

Comments

It should be 3. Those are ${\{ \epsilon, 1, 010\}}$.