Which one of the following statements is equivalent to the following assertion? Turing machine $M$ decides the language $L \subseteq \{0,1\}^*$

By definition, a Turing machine $M$ is said to decide a language $L \subseteq \Sigma^*$ (where $\Sigma = \{0,1\}$) if:

1. $M$ halts and accepts every string $w \in L$.

2. $M$ halts and rejects every string $w \notin L$ (i.e., every string $w \in \Sigma^* - L$).

Thus, $M$ accepts all strings in $L$ and rejects all strings in $\{0,1\}^* - L$.

Hence, option (D) is the correct statement.