A problem in which an

equivalence relation is deinfed over every pair of

elements in a

set S.

Let the relation be represented by the '~' character

a ~ b is either true or false and satisfies the properties of an

equivalence relation
ex:

S is a set of computers

~ = "is connected to"

Say we want to know if two computers a and b are connected. (a ~ b?). These types of

problems are most easily solved through the use of the

disjoint set.

*Note:* This requires that the connections be two way (symmetric), transitive (i.e. a is connected to b, which is connected to c, so a is connected to c.), and reflexive (a is connected to itself). These stipulations, which might seem obvious, are required to satisfy the requirements of an equivalence relation.