Discrete math-presentation
- 2. Presented by Muzahidul Islam ID: 152-15-5585 Anirudha Dhar Parash ID: 152-15-5742 S.M.Zahidul Islam ID: 152-15-5925 Sharuk Ahmed ID: 152-15-5796
- 3. HISTORY OF SETS The theory of sets was developed by German mathematician Georg Cantor (1845-1918). He first encountered sets while working on “Problems on Trigonometric Series” . SETS are being used in mathematics problem since they were discovered.
- 4. SETS Collection of object of a particular kind, such as, a pack of cards, a crowed of people, a cricket team etc. In mathematics of natural number, prime numbers etc.
- 5. A set is a well defined collection of objects. Elements of a set are synonymous terms. Sets are usually denoted by capital letters. Elements of a set are represented by small letters.
- 6. SET-BUILDER FORM In set-builder form, all the elements of a set possess a single common property which is not possessed by an element outside the set. e.g. : set of natural numbers k k= {x : x is a natural number}
- 7. EXAMPLE OF SETS IN MATHS N : the set of all natural numbers Z : the set of all integers Q : the set of all rational numbers R : the set of all real numbers Z+ : the set of positive integers Q+ : the set of positive rational numbers R+ : the set of positive real numbers.
- 8. TYPES OF SETS Empty sets. Equal sets. Subset. Finite &Infinite sets. Power set. Universal set.
- 9. THE EMPTY SET A set which doesn't contains any element is called the empty set or null set or void set, denoted by symbol ϕ or { }. e.g. : let R = {x : 1< x < 2, x is a natural number}
- 10. EQUAL SETS Given two sets K & r are said to be equal if they have exactly the same element and we write K=R. otherwise the sets are said to be unequal and we write K=R. e.g. : let K = {1,2,3,4} & R= {1,2,3,4} then K=R
- 11. SUBSETS A set R is said to be subset of a set K if every element of R is also an element K. R ⊂ K This mean all the elements of R contained in K.
- 12. FINITE & INFINITE SETS A set which is empty or consist of a definite numbers of elements is called finite otherwise, the set is called infinite. e.g. : let k be the set of the days of the week. Then k is finite let R be the set of points on a line. Then R is infinite
- 13. POWER SET The set of all subset of a given set is called power set of that set. The collection of all subsets of a set K is called the power set of denoted by P(K).In P(K) every element is a set. If K= {1,2} P(K) = {ϕ, {1}, {2}, {1,2}}
- 14. UNIVERSAL SET Universal set is set which contains all object, including itself. e.g. : the set of real number would be the universal set of all other sets of number. NOTE : excluding negative root