TOC: empty language and epsilon

Question

What is  ∅  U  ∅* ?

a) ∅

b) ϵ

c) Both a and b can be answer

d) Neither a nor b

Answer 1

• ∅  U  ∅* = { } U {ϵ} = {ϵ}
• ∅  $\cap$  ∅* = { } $\cap$ {ϵ}  = { } = ∅
• ∅  U  ϵ* = { } U {ϵ} = {ϵ}

Answer 2

We know that,

 RE + ∅ = RE and ∅* = ϵ , RE is Regular expression

So from the given question

∅  U  ∅* which is nothing but  ∅  + ∅*

Therefore

∅  +  ϵ =  ϵ

Hence,  Option B is the correct answer. Correct me if iam Wrong.

Answer 3

ANS is epsilon because here phi* which is equal to epsilon ie empty string.