Sets

14. SUMMARY

A summary of the basic concept of set theory is as follows:

 A set is any well-defined list, collection, or class of objects.

 Given a set A with elements 1,3,5,7 the tabular form of representing this set is A = {1, 3, 5, 7}.

 The set-builder form of the same set is A = {x| x = 2n + 1,0 ≤n≤3}

 Given the set N = {2,4,6,8,....} then N is said to be infinite, since the counting process of its elements will never come to an end, otherwise it is finite

 Two sets of A and B are said to be equal if they both have the same elements, written A = B

 The null set,∅ , contains no elements and is a subset of every set

 The set A is a subset of another set B, written A⊂B, if every element of A is also an element of B, i.e. for every x∈A then x∈B

 If B⊂A and B≠A, then B is a proper subset of A

 Two sets A and B are comparable if A⊂B and B⊂A

 The power set 2² of any set S is the family of all the subsets of S

 Two sets A and B are said to be disjoint if they do not have any element in common, i.e their intersection is a null set.