regular expression

Question

Let ‘r’ be a regular expression, is there exists any 'x' which satisfies property r + x = x ?

Answer 1

No there doesnt exist an X for which R+X = X

But There exists an X for which R.X = X  ie X is Empty set...Here X is also called an annhilator.

Comments

If X is Σ* ?

---

you cannot generalise it to Σ*....If R belongs to (a.b) and X belong to (c,d) Now see...

But when you take concatenation...Whatever the R maybe when X = empty set you get result as X