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Language L1 is defined by the grammar: S1 → aS1b | ε Language L2 is defined by the grammar: S2 → abS2 | ε Consider the following statements: P: L1 is regular Q: L2 is regular Which one of the following is TRUE?

1. Both P and Q are true
2. P is true and Q is false
3. P is false and Q is true
4. Both P and Q are false

Correct answer: P is false and Q is true

Solution

L1 generates a^n b^n, which is not regular (requires matching counts, provable by pumping lemma). L2 generates (ab)^n = (ab)*, which is regular. So P is false and Q is true.

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