In mathematics, two sets are disjoint when they have no elements in common. For example, the sets { 1 , 3 } {\displaystyle \{1,3\}} and { 2 , 4 } {\displaystyle \{2,4\}} are disjoint, but the sets { 1 , 3 } {\displaystyle \{1,3\}} and { 1 , 5 } {\displaystyle \{1,5\}} are not disjoint.