1

In a rowing
regatta there is a race involving six coxed eights. In each of the
following cases, say whether the relation is an equivalence relation
in the domain consisting of the competitors in the race, and, if it
is, how many equivalence classes there are and how many members there
are in each class: 

(i)

x rows in
the race in the same boat as y


(ii) 
x rows in
the race against a boat containing y


(iii)

x rows in
the race in the same position as y


(iv)

x
rows in the race and so does y
