Presentation on set in discrete mathe
- 1. Presentation on Set in Discrete Math Our Members:
- 2. Out Line 1. What is Set. 2. History of Set. 3. Method of Set. 4. What is Venn Diagram. 5. History of Venn Diagram. 6. Type of Set . 7. Type of Set. 8. Type of Set. 9. Operation of Set. 10. Union Set. 11. Interstation of Set. 12. Compliments of Set.
- 3. 1. What is Set A set is an unordered collection of different elements. A set can be written explicitly by listing its elements using set bracket. If the order of the elements is changed or any element of a set is repeated, it does not make any changes in the set.
- 4. 2.History of Set The famous German mathematician George Cantor (1845-1918) explained the first conception about the set. He created an invincible set of ideas, triggered the math script, and his set was known as Set Theory.
- 5. 3.Method of Set Roster or Tabular Form: The set is represented by listing all the elements comprising it. The elements are enclosed within braces and separated by commas. Example 1 − Set of vowels in English alphabet, A={a,e,i,o,u}A={a,e,i,o,u} Example 2 − Set of odd numbers less than 10, B={1,3,5,7,9}B={1,3,5,7,9} Set Builder Notation: The set is defined by specifying a property that elements of the set have in common. The set is described as A={x:p(x)}A={x:p(x)} Example 1 − The set {a,e,i,o,u}{a,e,i,o,u} is written as − A={x:x is a vowel in English alphabet}.
- 6. 4. What is Venn Diagram A Venn diagram (also called primary diagram, set diagram or logic diagram) is a diagram that shows all possible logical relations between a finite collection of different sets
- 7. 5.History of Veen Diagram Venn diagram, invented in 1880 by John Venn, is a schematic diagram that shows all possible logical relations between different mathematical sets.
- 8. 6. Type of Set Empty Set: A set that contains no members is called the empty set or null set . The empty set is written as { } or ∅. Finite Set: A set is finite if it consists of a definite number of different elements. If W be the set of people living in a town, then W is finite. Infinite Set: An infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. The set of all integers, {..., -1, 0, 1, 2, ...}, is a count ably infinite set. Equal Set: Equal sets are sets which have the same members. If P ={1,2,3}, Q={2,1,3}, R={3,2,1} then P=Q=R.
- 9. 7. Type of Sets Subset: Sets which are the part of another set are called subsets of the original set. For example, if A={1,2,3,4} and B ={1,2} then B is a subset of A it is represented by . Power Set: If ‘A’ is any set then one set of all are subset of set ‘A’ that it is called a power set. Example- If S is the set {x, y, z}, the power set of S is {{}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}. Universal Set: A universal set is a set which contains all objects, including itself. Example-A={12345678} B={1357} C={2468} D={2367} Here A is universal set and is denoted by U.
- 10. 8. Type of Set Disjoint Set: Two sets A and B are called disjoint sets if they do not have even one element in common. Therefore, disjoint sets have the following properties − •n(A∩B)=∅n(A∩B)=∅ •n(A∪B)=n(A)+n(B)n(A∪B)=n(A)+n(B) Example− Let, A={1,2,6}A={1,2,6} and B={7,9,14}B={7,9,14}, there is not a single common element, hence these sets are overlapping sets.
- 11. 9. Operation of Set 1. Union Set. 2. Interstation of Set. 3. Compliments of Set.
- 12. 10. Union Set The union of two sets would be wrote as A U B, which is the set of elements that are members of A or B, or both too. Example:
- 13. 11. Interstation of Set Intersection are written as A ∩ B, is the set of elements that are in A and B. For example:
- 14. 12. Compliments of Set If A is any set which is the subset of a given universal set then its complement is the set which contains all the elements that are in but not in A. Example: