X={2,5,8}, Y={10,16,24,30}
When a∈X=2, then 2Rb for all b∈Y is true, that is, 2 is a factor of all elements in Y (all elements of Y are even integers).
When a∈X=5, then 5Rb is not true for all b∈Y, but 5R10 and 5R30 are true.
When a∈X=8, then 8Rb is not true for all b∈Y, but 8R16, 8R24 and 8R30 are true.
In mapping X onto Y when n(X)<n(Y) R cannot be a function because there can be no more than n(X) elements in Y. n(Y)≤n(X) is permissible for a function, that is, many different elements of X can map to the same element in Y, but the same element of X can only map to a unique element of Y.
If all the elements of Y were multiples of 40 (LCM of 2, 5 and 8), then aRb would be true ∀a,b, but R could still not be a function, because there are more elements in Y than in X.