Given two sets of items then if any item is common to any set then the result of applying ''consolidation'' to those sets is a set of sets whose contents is:
*  The two input sets if no common item exists between the two input sets of items.
*  The single set that is the union of the two input sets if they share a common item.

<br>Given N sets of items where N>2 then the result is the same as repeatedly replacing all combinations of two sets by their consolidation until no further consolidation between set pairs is possible.
If N<2 then consolidation has no strict meaning and the input can be returned.

;'''Example 1:'''
:Given the two sets <tt>{A,B}</tt> and <tt>{C,D}</tt> then there is no common element between the sets and the result is the same as the input.
;'''Example 2:'''
:Given the two sets <tt>{A,B}</tt> and <tt>{B,D}</tt> then there is a common element <tt>B</tt> between the sets and the result is the single set <tt>{B,D,A}</tt>.  (Note that order of items in a set is immaterial: <tt>{A,B,D}</tt> is the same as <tt>{B,D,A}</tt> and <tt>{D,A,B}</tt>, etc).
;'''Example 3:'''
:Given the three sets <tt>{A,B}</tt> and <tt>{C,D}</tt> and <tt>{D,B}</tt> then there is no common element between the sets <tt>{A,B}</tt> and <tt>{C,D}</tt> but the sets <tt>{A,B}</tt> and <tt>{D,B}</tt> do share a common element that consolidates to produce the result <tt>{B,D,A}</tt>. On examining this result with the remaining set, <tt>{C,D}</tt>, they share a common element and so consolidate to the final output of the single set <tt>{A,B,C,D}</tt>
;'''Example 4:'''
:The consolidation of the five sets:
::<tt>{H,I,K}</tt>, <tt>{A,B}</tt>, <tt>{C,D}</tt>, <tt>{D,B}</tt>, and <tt>{F,G,H}</tt>
:Is the two sets:
::<tt>{A, C, B, D}</tt>, and <tt>{G, F, I, H, K}</tt>
<br>
'''See also'''
* [[wp:Connected component (graph theory)|Connected component (graph theory)]]
* [[Range consolidation]]
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