Given the recursively enumerable language (LRE), the context sensitive…

Correct relationship: Deterministic context-free ⊆ Context-free ⊆ Context-sensitive ⊆ Recursive ⊆ Recursively enumerable

• Deterministic context-free ⊆ Context-free: every deterministic pushdown automaton is a pushdown automaton, so every deterministic context-free language is context-free. There exist context-free languages that are not deterministic context-free (for example, certain palindrome languages).

• Context-free ⊆ Context-sensitive: any context-free language can be generated by a context-sensitive grammar, and there are context-sensitive languages that are not context-free (for example, {a^n b^n c^n}).

• Context-sensitive ⊆ Recursive: context-sensitive languages are exactly those decided by linear-bounded automata, which always halt, so every context-sensitive language is recursive (decidable).

• Recursive ⊆ Recursively enumerable: every decider is also a recognizer, so every recursive language is recursively enumerable. There are recursively enumerable languages that are not recursive (for example, the halting problem).

Therefore the correct ordering from smallest to largest is: Deterministic context-free ⊆ Context-free ⊆ Context-sensitive ⊆ Recursive ⊆ Recursively enumerable