Question: How to prove the language if a language is context free Language without using Pumping Lemma? Assume there exist languages: L 1 ={ 1 a

How to prove the language if a language is context free Language without using Pumping Lemma?

Assume there exist languages: L1={ 1a0a2b1b | a>0,b>0} and L2={ 1a0a2a1b | a>0,b>0}.

1. Prove one of them is context-free by applying a context-free grammar that defines this language

2. Prove another is not context-free by using closure properties of context-free and regular languages.

Do not use pumping lemma!

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