Solution

The correct answer is 3) C and D Only.

Key Points

• Regular languages and context-free languages are both classes of formal languages used in automata theory and formal language theory.
• Option A: Both regular languages and context-free languages are closed under union operation. This means if L1 and L2 are regular (or context-free) languages, then L1 ∪ L2 is also a regular (or context-free) language.
• Option B: Both regular languages and context-free languages are closed under concatenation operation. This means if L1 and L2 are regular (or context-free) languages, then L1L2 (concatenation of L1 and L2) is also a regular (or context-free) language.
• Option C: Regular languages are closed under intersection operation, but context-free languages are not necessarily closed under intersection. This means if L1 and L2 are regular languages, then L1 ∩ L2 is also a regular language, but if L1 and L2 are context-free languages, L1 ∩ L2 may not be context-free.
• Option D: Regular languages are closed under complementation operation, but context-free languages are not necessarily closed under complementation. This means if L is a regular language, then its complement L' is also a regular language, but if L is a context-free language, L' may not be context-free.
• Option E: Both regular languages and context-free languages are closed under Kleene star operation. This means if L is a regular (or context-free) language, then L* (Kleene star of L) is also a regular (or context-free) language.

Additional Information

• Closure properties are important in the study of formal languages as they help in understanding the limitations and capabilities of different language classes.
• Understanding these closure properties aids in the design of efficient algorithms for language recognition and parsing.
• Regular languages can be recognized by finite automata, while context-free languages can be recognized by pushdown automata.