Answer

Correct Option: (iii) The union of two CFLs is context-free

Explanation

CFL closure:

Operation	Closed?	Example
Union $L_1 \cup L_2$	Yes	$S \rightarrow S_1 \mid S_2$
Intersection $L_1 \cap L_2$	No	$a^n b^n c^* \cap a^* b^n c^n = a^n b^n c^n$ not CFL
Complement	No	Follows from De Morgan
Every CFL is DPDA	No	$\{a^n b^n\} \cup \{a^n b^{2n}\}$ is CFL but not DCFL
Intersection of 2 CFLs is CFL	No

Thus only union is guaranteed.

Options:

• (i) Intersection → false
• (ii) Every CFL is DPDA → false (DCFL ⊂ CFL)
• (iii) Union → true ✓
• (iv) Complement → false

Final Answer

Union of two CFLs is CFL → Option (iii).