The two regular expressions abc and abc(φ)* are equivalent. (T/F)

Question

I keep going back and forth on this question. Obviously both expressions will always begin with "abc" but I am not sure what effect the addition of Phi will have on the expression. It is an empty set, yet "abc" does not contain the empty set so they would not be equivalent?

Thanks for any help!

Answer 1

If in your notation $\varphi$ denotes the empty string, they are equivalent. If $\varphi$ is anything else, they are not.