d(P, A) = d(P, B) can be rewritten as |PA| = |PB|. This means that the distance from point P to A is equal to the distance from point P to B. To find the set of all points equidistant from A and B, we can use the midpoint formula to find the coordinates of the midpoint M of line segment AB. Then, we can use the distance formula to find the distance from M to any point P. This distance will be the same as the distance from P to A and from P to B, so the set of all points equidistant from A and B is the sphere with center M and radius |MA| (or |MB|).