Answer

Correct Option: (iii) Intersection

Explanation

Closure properties of Context-Free Languages (CFLs):

Operation	Closed?
Union $L_1 \cup L_2$	Yes – $S \rightarrow S_1 \mid S_2$
Concatenation $L_1L_2$	Yes – $S \rightarrow S_1S_2$
Kleene star $L^*$	Yes – $S \rightarrow SS_1 \mid \epsilon$
Intersection $L_1 \cap L_2$	No
Complement $\overline{L}$	No

Counterexample for intersection:
$L_1 = \{a^n b^n c^m \mid n,m\ge0\}$ (CFL), $L_2 = \{a^m b^n c^n \mid n,m\ge0\}$ (CFL)
$L_1 \cap L_2 = \{a^n b^n c^n\}$ which is not CFL (pumping lemma).

Since De Morgan: $L_1 \cap L_2 = \overline{\,\overline{L_1}\cup\overline{L_2}\,}$, non-closure under intersection implies non-closure under complement.

Final Answer

CFLs are NOT closed under Intersection → Option (iii).