A course book presents the bolded part of the below sentence pairs as examples of fragments:
I am planning to go for a new smart phone. The one I am using is dead slow.
An MNC has expressed interest in recruiting our students for back office positions. Their HR managers are expected to visit our college soon.
But my instinct is that both of them are full sentences, not fragments. They do not come within the definition of a fragment, i. e. "A SENTENCE FRAGMENT fails to be a sentence in the sense that it cannot stand by itself. It does not contain even one independent clause".
In grammar anaphora is the use of a word referring back to a word used earlier in a text or conversation, to avoid repetition. In both the "sentences/fragments", there are anaphoric pronouns.
Can the anaphoric pronouns make sentences fragments?
Are they actually sentence fragments?