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In [[combinatorics|combinatorial]] mathematics, given a collection ''C'' of disjoint [[set theory|sets]], a '''transversal''' is a set containing exactly one element from each member of the collection: it is a [[Section (category theory)|section]] of the [[quotient map]] induced by the collection. If the original sets are not disjoint, there are several different definitions. One variation is that there is a [[bijection]] ''f'' from the transversal to ''C'' such that ''x'' is an element of ''f''(''x'') for each ''x'' in the transversal. A less restrictive definition requires that the transversal just has a non-empty intersection with each member of ''C''.
As an example of the disjoint-sets meaning of ''transversal'',
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