Which of the following languages is generated by the given grammar? $$S \longrightarrow aS \mid bS \mid \varepsilon$$

Given the grammar rules:

From the start symbol $S$:

• By choosing $S \rightarrow aS$, an 'a' is prefixed.

• By choosing $S \rightarrow bS$, a 'b' is prefixed.

• By choosing $S \rightarrow \varepsilon$, the derivation terminates.

Thus, at any step, either 'a' or 'b' can be generated independently, and the derivation can terminate at any length including $0$ (the empty string $\varepsilon$). This generates any string consisting of arbitrary combinations of $a$'s and $b$'s.

Therefore, the language generated is $(a+b)^* = \{a, b\}^*$, which corresponds to option (D).