Question 17 Which of the following statement FALSE:

Statement A is FALSE: CFLs are closed under union but NOT closed under intersection. Statement C is TRUE: regular languages ARE closed under complement (DFA can be converted to complement by swapping accept/non-accept states). Statement B is TRUE: subset is not a standard closure property operation. Therefore, the false statements are A and C, making option 'A and C' correct.

Step-by-step Derivation:
Analyze each statement:

Statement A: 'CFLs are closed under Union and Intersection'

• CFLs ARE closed under union: if L1 and L2 are CFLs, then L1 ∪ L2 is a CFL (merge grammars with new start rule: S → S1 | S2)
• CFLs are NOT closed under intersection: counterexample: L1 = {a^n b^n c^m} and L2 = {a^m b^n c^n}, their intersection is {a^n b^n c^n}, which is context-sensitive, not context-free
• STATEMENT A IS FALSE (claims closure under both; intersection fails)

Statement B: 'CFLs are not closed under subset operation'

• Subset is not a closure property; this statement is oddly phrased but technically TRUE in that CFLs lack a meaningful 'subset' closure property
• STATEMENT B IS TRUE

Statement C: 'Regular languages are closed under complement'

• Regular languages are closed under complement: given a DFA M accepting language L, create DFA M' by swapping accepting and non-accepting states to accept the complement L'
• STATEMENT C IS TRUE

False statements: A and C (option D)