Consider the following language families: 𝐿1≡ The context-free languages 𝐿2≡…

Answer: L1 ⊆ L2 ⊆ L4 ⊆ L3

• Context-free ⊆ Context-sensitive: Every context-free language can be generated by a context-sensitive grammar or recognized by a linear-bounded automaton simulated appropriately, so all context-free languages are context-sensitive.

• Context-sensitive ⊆ Recursive (decidable): Languages accepted by linear-bounded automata are decidable (the machine always halts), so every context-sensitive language is recursive.

• Recursive ⊆ Recursively enumerable: Any decidable language can be accepted by a Turing machine that halts on all inputs, therefore every recursive language is recursively enumerable.

Thus the correct inclusion chain is: context-free (L1) ⊆ context-sensitive (L2) ⊆ recursive (L4) ⊆ recursively enumerable (L3).