the pumping lemma is not hard to understand , its the extended version of pigeon hole priciple . iam writing here the answer please look and if you have any doubt ask me
1. since before this you have to understand the pigionhole priciple as this will come handy to understand the what actually happening in the pummping lemma. say the given language is regular , since its regular , it could be finite or infinite depending upon the langugage . bear with me you will understand . if the langugae is finite you could easily tell that the languge i regular or not but problem arises when you get an infinite language. now as said we assumed that the language is regular and if its infinite or finite in both cases we could contruct its dfa. Now dfa has finite states now take a string that belongs to the language but have length greater than total states of dfa , to put this string in dfa we have to put more than one string in a single state that is a loop exists . since the loop can exist on any of the given alphabet we need to choose different possiblities , but this can be done easily if you can look to the language given . now since we have loop it should accept more string of the same alphabets when looped and if not then the langugage is not regular if it does then the language is regular but look to cover other alphabet if looped and rule all the possiblities . the above method is formally called as pummpimg lemma , and because of above language its easy to prove irregular languge irregular rather than regular as regular
