Answer is 2^4=16. The main confusion here is whether to include phi in the relation or not. well, we will count phi.
clearly by law of implication, for some pair say (1,2) , if we try (1,2) ∈S but 1!=2. so this is T->F resulting in F. so (1,2) can not belong to S. now phi is an empty relation it has no element so for phi , (x,y)∈S fails and we know F->anything is True so Phi will be in the relation.
only four pairs namely (0,0),(1,1),(2,2),(3,3),and (4,4) are taken as these apir satisfy the condition x=y.
hence the nos relations which is the cartesian product are as follows like (x,y)
1 2 3 4 (y coordinate )
these are 16 relations which is equal to 2^4 .