language

Question

1. ϕ
2. Σ*
3. L
4. X

Comments

Is it B?

---

d?

---

how B? @prashant jha 1

Answer 1

a)Not possible

b)Correct answer  (L U X)

Regular expression for L=(0+1)*1
Regular expression for X=ϵ+0* +1(0+1)*+0(0+1)*                                                                                                                                    
(L U X)= (0+1)*1 + ϵ+0* +1(0+1)*+0(0+1)* = (0+1)*

c)String 10 is accepted by (L U X) not ending with 1 (not equal to L)
d) It also seems correct I can't find any string accepted in (L U X) that is not there in X.

Some pls check little bit confused.

Answer 2

All options seem wrong!

L is a language ending with 1 and on close inspection of X,

X is a language with even number of 1's.

So (L union X) gives strings which match none of the options.

A) Not possible

B) Both L and X can't generate string '01' so not possible

C,D) Strings of L and X are few same few different so not possible

Comments

@ Manjyot
B) is not answer but 01 string accepted by (L U X) i.e L accepts 01 followed by X to ϵ

D)   Regular expression for L=(0+1)*1
       Regular expression for X=ϵ+0* +1(0+1)*
       now X covers String starting with 0 or 1 and ending with 1 so X covers all possible strings             accepted by L

---

But how can we derive '01' from the grammar X? I am unable to derive it through productions mentioned

---

Yes you are right that 01 is not accepted by X but question asks for( L union X) and from L we can derive 01 and union will contain 01

---

Question seems to be incorrect even B is not satisfying all the conditions

Answer given by made easy is B