Q19

Given a set:

$$S = \left\{x \mid \text{ there is an x-block of 5's in the decimal expansion of } \pi\right\}$$

(Note: $x$-$block$ is a maximal block of $x$ successive $5$'s) Which of the following statements is true with respect to $S$? No reason to be given for the answer. $S$ is regular $S$ is recursively enumerable $S$ is not recursively enumerable $S$ is recursive Given that a language $L_1$ is regular and that the language $L_1 \cup L_2$ is regular, is the language $L_2$ always regular? Prove your answer.