The definition
You may find what you're looking for in the section 9.5 about properties:
Properties are StructuralFeatures that represent the attributes of Classifiers, the memberEnds of Associations, and the parts of StructuredClassifiers.
The UML specs underline that it applies as well to associations ends (section 11.5.3.1, p.200):
Subsetting of Association ends has the meaning specified for Property (see 9.5.3).
More precisely, the semantics of subsetting are defined in section 9.5.3 (page 112):
A Property may be marked as the subset of another subsettedProperty. In this case, calculate a set by eliminating duplicates from the collection of values denoted by the subsetting property in some context. Then that set shall be included in (or the same as) a set calculated by eliminating duplicates from the collection of values denoted by the subsettedProperty in the same context.
Remark: There is no definition of subsetting an association as a whole (i.e. beyond the association end, like in your example). But a paragraph on specialization reasons on sets of links (i.e the tuples of classified values at each end of the association) instead of sets of values. The existing definition could easily be applied likewise.
Application to your example
Statement 4 appears correct. Take a person A that is member of the club C1, C2, C3, C4, and at the same time leader of C1:
The definition requires that the set of unique values in the subsetting property isLeaderOf, i.e.{ C1 } shall be included in the set of unique values of the subsetted property isMemberOf, i.e. { C1, C2, C3, C4 }. The upper bound of the multiplicity of isLeaderOf does not allow to be leader of more than one club. So it'll stay C1 only. The inclusion requirement implies that if A is leader of C1, C1 must be among the values of club memberships. You could add as many more club memberships, as you want, as long as C1 remains in. Even adding multiple C1 memberships would not change the truth of your statement.
In your example, the upper bound 1 simplifies the reasoning. In the more general case, values of the sets are not necessarily unique. So some care is required when making claims about lower and upper bound of multiplicities, since duplicate values could create tricky situations. However, the inclusion requirement is purposely defined based on unique values.
Statement 3 is more tricky and requires deduction: You didn't subset the opposite association end. This means that a club C could have members M1, M2, M3, and could have a leader L, but nothing guarantees that the leader is member of the same club; You could even have a leader without any member:
- Subsetting
leader as well would easily solve the issue.
- But even as it is, leader and members being persons, and thanks to the upper bound of 1, we can deduce that such a situation would not be possible, and consequently that statement 3 is true as well.
