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Help me for this question by using the properties of regular language, please stven L= {oll p is prime? is not regular....

Help me for this question by using the properties of regular language, please

stven L= {oll p is prime? is not regular. rove using the properties ofregu L aIpl are not Prineinet egular. Usin, weproperti

stven L= {oll p is prime? is not regular. rove using the properties ofregu L' aIpl are not Prineinet egular. Usin, wepropertiestregudartangu呼es.NoT pumping-lemma FHank yuvery Muck!
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Proof by contradiction -

Let L' = {apbq | p,q are not prime} be a regular language.

Then, by concatenation L' = L1.L2 where L1 = {ap | p is not prime} and L2 = {bq | q is not prime}
L1 and L2 are regular languages. (concatenation property)
L1' = {ap | p is prime} therefore L1' is also regular but this contradicts the given statement that {ap | p is prime} is not regular. (complement property)

Hence, our assumption that {apbq | p,q are not prime} is a regular language is also wrong.
Hence, proved.
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