Statistics-For a language L, let Init(L) = {x | xy ∈ L for some y ∈ Σ∗}

For a language L, let Init(L) = {x | xy ∈ L for some y ∈ Σ∗}. Let r, s, rI and sI be regular expressions for the languages R, S, Init(R), and Init(S) respectively. Using only these regular expressions and the operations “+, concatenation, and ∗”, give expressions for the following languages and very briefly justify your answers:

(a) (4 points) Init(R ∪ S).

(b) (4 points) Init(RS).

(c) (4 points) Init(R∗).

Please help!!!