Suppose there is a three-cluster solution and a two-cluster solution both obtained using the same algorithm. Observation X and observation Y are in the same cluster in the three-cluster solution. Which of the following statements are true?

Select one:

a.

Observation X and observation Y must be in the same cluster in the two-cluster solution if k-means clustering was used.

b.

Observation X and observation Y must be in the same cluster in the two-cluster solution if the centroid method was used.

c.

Observation X and observation Y must be in different clusters in the two-cluster solution if k-means clustering was used.

d.

Observation X and observation Y can be in the same cluster or in different clusters in the two-cluster solution and this does not depend on the clustering algorithm that has been used.

e.

Observation X and observation Y must be in different clusters in the two-cluster solution if the centroid method was used.