Question 7934 – Theory-of-Computation

Strings in L₁ = {ϵ, c, cc, …., ab, aabb,…., abc, abcc,…, aabbc, aabbcc, aabbccc,..}
Strings in L₂ = {ϵ, a, aa, …., bc, bbcc,…., abc, aabc,…, abbcc, aabbcc, aaabbcc,..}
Strings in L₁ ∪ L₂ ={ϵ, a, aa, .., c, cc,.. ab, bc, …, aabb, bbcc,.., abc, abcc, aabc,…}
Hence (L₁ ∪ L₂) will have either (number of a’s = equal to number of b’s) OR (number of b’s = number of c’s).
Hence (L₁ ∪ L₂) is CFL.
Strings in L₁ ∩ L₂ = {ϵ, abc, aabbcc, aaabbbccc,…}
Hence (L₁ ∩ L₂) will have (number of a’s = number of b’s = number of c’s)
i.e., (L₁ ∩ L₂) = {aⁿbⁿcⁿ | n ≥ 0} which is CSL.