Answer:
The sentence that does not contain an antecedent is sentence A.
Step-by-step explanation:
An antecedent is an earlier clause, phrase, or word to which a pronoun, noun or another word refers. In the sentence above, the determiners "his" and "her" do not have any antecedent to refer to. That is to say, there are no words earlier in the clause to which they refer. We can tell that "his" refers back to a man and "her" to a woman, yet that is all the information we have.