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

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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Help me for this question by using the properties of regular language, please stven L= {oll p is prime? is not regular....
Using closure properties or pumping lemma, prove or disprove if this language is regular: L = {(a, b)*c(a, b)*}
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular language L, there exists a pumping length p such that, if s€Lwith s 2 p, then we can write s xyz with (i) xy'z E L for each i 2 0, (ii) ly > 0, and (iii) kyl Sp. Prove that A ={a3"b"c?" | n 2 0 } is not a regular language. S=
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular...
I'm trying to show that L6={cnambp:n+m=p,p?6} is not regular. I need a little help, I was practicing the pumping lemma, and I encountered this language, I saw these conditions and got totally confused, what to do now? Earlier I showed that L5={anbn:n?0} is not regular. In this Language it was very simple to choose w, namely w=apbp, where p is the pumping length. But this new Language is complicated, so I thought you guys could help me out.
Use the pumping lemma to show that the following language is not regular: L = {bi ajbi : i, j ≥ 1}
4. (15 points) Using the pumping lemma for regular languages show that the following language is not regular
Can someone use pumping Lemma to show if these are regular
languages or not
c) Is L regular? give a finite automaton or prove using pumping lemma. (d) Is L context-free? give a context-free grammar or pushdown automaton, otherwise pr using pumping lemma. (16 pts)Given the set PRIMES (aP | p is prime (a) Prove that PRIMES is not regular. (b) Prove that PRIMES is not context-free. (c) Show if complement of PRIMES (PRIMES ) is regular or not. d)...
6. (10 pts) Is L regular? Either prove that it is not regular using pumping lemma, or describe an RE for it. The alphabet of the language is 10,1, +,-) L = { x = y + z | x, y, z are binary integers, and x is the sum of y and z }. For example, strings 1000 = 101 + 11, 0101 = 010 + 11, and 101 = 101 + 0 are in the language, but strings...
Prove that the language L = {a^pb^qc^r|p,q,r >=1 and pq = r} is not context free using pumping lemma. I honestly just need help coming up with a string that works, thanks.
SUBJECT:THEORY OF COMPUTATION
CAN SOMEONE PLEASE HELP ME I HAVE POSTED IT REPEATEDLY
AND I KEEP GEETING INCOMPLETE / INCORRECT ANSWER . I WILL GIVE YOU
A HIGH REVIEW IF YOU HELP ME AND IT IS DONE PROPERLY !
Note: Please show/explain all cases clearly for the pumping lemma and describe how your Turing machine works for each state transition. Problem 1: Non-context-free languages and Tining Machine Models B5] context-free: 쉑: Use the pumping lemma for context-free languages to show...
3. (20 pt.) Prove that the following language is not regular using the closure properties of regular languages. C = {0"1"|m,n0 and mon} Hint: find a regular language L such that CNL is not regular and use the closure properties of regular languages to show that this means that C is not regular.