People are having some kind of a day fair.
The people are attending a church service.
Attending a church service is generally for religious beliefs; day fair could be a variety of things. While a day fair could be a type of church service; i would simply believe they are 2 different events in the above sentences.
exists e1 x1 x2 x3 x4.(Theme(e1,x2) & Actor(e1,x1) & v_have(e1) & of(x2,x3) & n_fair(x3) & of(x3,x4) & n_day(x4) & n_kind(x2) & n_people(x1))
exists e1 x1 x2 x3.(n_people(x1) & Theme(e1,x2) & Actor(e1,x1) & v_attend(e1) & n_service(x2) & of(x2,x3) & n_church(x3))