I found this solution on Wikipedia. Shouldn't it say: j>n≥ 0 Because the intersection are elements that are common in both languages.
Consider the languages L1 and L2 defined by L1={a^(n)b^(n)c^(j)| n,j ≥ 0} and L2 = {a^(j)b^(n)c^(n): n,j ≥ 0}. They are both context-free. However, their intersection is the language L = {a^(n)b^(n)c^(n)| n ≥ 0}.
No it should not. There is no relation between j and n. In L1 the only condition is equal number of a's and b's. Whether the number of c's is more or less is immaterial. Similarly in L2, it is equal number of b's and c's. Whether the number of a's is more or less (than the number of b's and c's) is not important. However the intersection will have those strings which fall in both L1 and L2, i.e. (equal number of a's and b's) AND (equal number of b's and c's) which implies equal number of a's, b's and c's.
