Let X = {3, 6, 12, 24, 48}. Let

Question

Let X = {3, 6, 12, 24, 48}. Let <= be the partial order defined by X <= Y if X divides Y. Number of edges in the Hasse diagram of (X, <=) is

A. 3
B. 4
C. 9
D. None of the above

Accepted Answer

B. 4 A Hasse diagram shows only covering relations: an edge x -> y appears only when x divides y AND there is no element z in the set with x divides z and z divides y. The set {3,6,12,24,48} forms a chain 3|6|12|24|48 (each element is double the previous). A chain of 5 elements has exactly 4 consecutive covering pairs: (3,6), (6,12), (12,24), (24,48). All non-consecutive divisibility pairs have an intermediate element.

Let X = {3, 6, 12, 24, 48}. Let <= be the partial order defined by X <= Y if X divides Y. Number of edges in the Hasse diagram of (X, <=) is A. 3 B. 4 C. 9 D. None of the above