disjoint --- two sets are disjoint if their intersection is empty.
we use S denote collection of sets, S is also a set.
we use ∪S denote the set whose elements are the elements of all the sets in S.
power set--- if A is a set, the collection of all subset of A we called power set of A and denoted 2A.
partition --- a partition of set A is a subset of 2A , denoted ∏, satisfiy:
1) each element of ∏ is non-empty
2) distinct members of ∏ are disjoint
3) ∪∏=A
ordered pair --- denoted (a,b)
Cartesian product --- Cartesian product of two sets A and B denoted by A×B
relation --- n-ary relation on sets A1 … An is a subset of A1×…× An
function --- a fuction from a set A to a set B is a binary relation R on A and B.
directed graph --- the relation R can be represented by a directed graph.
reflexive --- if (a,a)∈R for each a∈A
symmetric --- if (a,b)∈R then (b,a)∈R
transitive ---if (a,b)∈R and (b,c)∈R, then (a,c)∈R
equivalence relation --- A relation that is reflexive, symmetric and transitive is called an equivalence relation
equivalence classes --- The clusters of an equivalence relation are called its equivalence classes.