Subset in a regular expression

Question

Is this true for every two regular expressions $G$ and $K$?

1. $(GG + K)^*$ is a subset of $(KGG)^*$ and

2. $(KGG)^*$ is also a subset of $(GG + K)^*$

Answer 1

Take $G = a$ and $K = b$. Then $aa$ matches $(GG + K)^*$ but not $(KGG)^*$. Thus (1) is not true.

However (2) is true, since $(KGG)^*$ is the infinite union of the sets $(KGG)^n$ (where $n \geqslant 0$) and $\underbrace{(KGGKGG \cdots KGG)}_{n \text{ times}}\ $ can be written as a product of $GG$ and $K$.