Prove a problem is NP-hard.

I am computer science lecturer with having experience of teaching for computing subjects at university level from 5 years I am at home in theory of computation with its contents such as regular expressions and f a d f a context free grammar pumping lemma Maurya machine MI machine NP problems in p hard problems proves graph problems and analysis of algorithm such as travelling salesman problem dynamic problem and greedy search algorithms etc, I can I correctly prove that the problem is non polynomial hard problem with the help of rules and cat graphs

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