Combinatorics

Equivalence relations is a very important concept in many branches of mathematics. An equivalence relation is a way to partition sets into subsets and equate elements with each other. The only requirements of an equivalence relation are that it must abide by the reflexive, symmetric and transitive laws.

Relating cards by suits in the deck of cards is one equivalence relation. Two cards are equivalent if they have the same suit. Card color, red or black, is another equivalence relation. In algebra, "equals," "greater than" and "less than" signs are examples of equivalence relations on numbers. These relations become important when we ask questions about subsets of a set of objects.