5.3.20.2. Set Operations on Collections without Duplicates

Assume that the example sets are A={a,b} and B={b,c,d}. Except for subset, equivalent, and disjoint, the result of a set operation is another set. Using the collection A and B, the different set operators produce the following:

UNION operation

All elements of A and B are united:

A UNION B = {a,b,c,d}

DIFFERENCE operation

The resulting collection contains all elements of the first set except for those that also appear in the second set. The system iterates over the elements of the second set and removes them from the first set one by one.

A DIFFERENCE B = {a}
B DIFFERENCE A = {c,d}

XOR operation

The resulting collection contains all elements of the first set that are not in the second set and all elements of the second set that are not in the first set:

A XOR B = {a,c,d}

INTERSECTION operation

The resulting collection contains all elements that appear in both sets:

A INTERSECTION B = {b}

SUBSET operation

Returns .true if the first set contains only elements that also appear in the second set, otherwise it returns .false:

A SUBSET B = .false
B SUBSET A = .false

EQUIVALENT operation

Returns .true if the first set contains only elements that also appear in the second set and the two sets have the same number of elements, otherwise it returns .false:

A EQUIVALENT B = .false
B EQUIVALENT A = .false

DISJOINT operation

Returns .true if there are no elements that appear in both sets, otherwise it returns .false:

A DISJOINT B = .false
B DISJOINT A = .false