Official answer: B) {(ab)n cbm1cbm2 cbmn n, m1, m2, , mn ≥ 1}
Context-Free Grammars and PDAsLet us analyze the derivations possible from the grammar:
From the production T→bT∣b, the non-terminal T generates any non-empty string of b's:
T⇒bm,m≥1 The start symbol S derives strings recursively:
Base case (n=1):
S⇒abcT⇒(ab)1cbm1,m1≥1 Recursive step:
S⇒abScT1⇒ab(abScT2)cT1⇒⋯⇒(ab)ncTncTn−1…cT1
Since each instance of Ti can independently derive a sequence of b's of length mi≥1, the language generated is:
{(ab)ncbm1cbm2…cbmn∣n,m1,m2,…,mn≥1}
Notice that the number of b's following each c can vary independently (m1,m2,…,mn), but there must be exactly n occurrences of ab at the beginning matched with n occurrences of the block cbmi.
Therefore, (B) is the correct option.