1. Sets, Relation and Functions A set is a collection of objects (elements) or a container of objects. Defining sets –Empty set (Ø): no elements –Universal set (U): all the elements in the universe of discourse. Representation of set –List up all of its members {1,2,3} –Listing the properties {x|1 ≤ x ≤ 2 and x is a real number.} –Procedure to generate the numbers of the set (recursive definition)

2. Basics of Set Equality of sets: They contain same elements Subset : Every element in A is also in B –If A is a subset of B then B is a superset of A –A is proper subset of B if A is a subset of B and A is not equal to B. Cardinality : size of the set Power set: the set of all subsets of a set A.

3. Set Operations Intersection of sets Union of sets Difference of sets Complement of set Ordered pair Cartesian product Families of sets Partition of a set

4. Relations A relation between A and B is a subset of AxB. If R is a relation b/w A and B and (a,b) belongs to R we write aRb and say that a is related to b. The Inverse Relation: R -1 = {(b,a):aRb} Composite Relations (SoR, To(SoR)) Example Name = {Adam, Bob, Eve} Position = {ECO, CTO, Eng} Salary = {1000, 500,} Tax = {63, 52, 45} Relations Name x Position Position x Salary Salary x Tax

5. Equivalence Relations R is an equivalence relation if R is reflexive, symmetric and transitive –Reflesive if and only if aRa for all a belongs to A –Symmetric if and only if aRb implies bRa for all a, b belongs to A –Transitive if and only if aRb and bRc implies aRc for all a, b, c belongs to A