premise: A man wearing a black hat is smiling on a street as other men and woman walk past. hypothesis: The man is greeting the people as he is walking on by.
entailment: A man singled out as smiling can be clearly referred to as 'the' man; greeting is a likely thing for a smiling person to be doing, as smiling is a common component of greeting; men and women are people; since the other people 'walk past', nothing is stopping the man from also 'walking on by'.