Answer

Correct Option: (i) a proper superset of CFLs (and (ii)/(iv) also true depending on option set)

Explanation

Recursive languages = Decidable languages = $L$ decided by TM that always halts.

Hierarchy:
$$\text{Regular} \subset \text{DCFL} \subset \text{CFL} \subset \text{CSL} \subset \text{Recursive} \subset \text{RE}$$

• (i) Proper superset of CFLs → True. Every CFL is recursive (PDA can be simulated by halting TM), but not vice versa (e.g., $a^n b^n c^n$ is recursive not CFL).
• (ii) Always recognizable (RE) → True, recursive ⊂ RE, so yes.
• (iv) Recognizable by TM → True (RE definition).
• (iii) also called Type-0 → False, Type-0 = RE, not Recursive (Type-1 is CSL, not Recursive either; Recursive is not a Chomsky type but decidable).

If single choice, (i) proper superset of CFLs is the intended answer. If multiple, (i),(ii),(iv) are true.

Final Answer

Recursive languages are proper superset of CFLs → Option (i) (also RE).