0
Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

# Dxc

4,165

Published on

6 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No

Are you sure you want to  Yes  No
• Good

Are you sure you want to  Yes  No
• Awesome Slide man thx bro

Are you sure you want to  Yes  No
Views
Total Views
4,165
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
297
3
Likes
6
Embeds 0
No embeds

No notes for slide

### Transcript

• 1. Introduction &#x2022; The theory of sets was developed by German mathematician George Cantor. &#x2022; A set is a collection of objects. &#x2022; Objects in the collection are called elements of the set. &#x2022; They are named by capital English alphabet.
• 2. Representation Of Sets&#x2022; Roster form and Set Builder form &#x2022; Roster Form- when the elements are written inside the set It is defined as a set by actually listing its elements, for example, the elements in the set A of letters of the English alphabet can be listed as A={a,b,c,&#x2026;&#x2026;&#x2026;.,z} separated by comas.
• 3. &#x2022; Set Builder Form- when we write a set in a straight form using underlying relations that binds them. &#x2022; Example- {x | x &lt; 6 and x is a counting number} in the set of all counting numbers less than 6. Note this is the same set as {1,2,3,4,5}.
• 4. Types Of Sets &#x2022; Empty Sets &#x2022; Finite Sets &#x2022; Infinite Sets &#x2022; Equal Sets &#x2022; Subsets &#x2022; Power Sets &#x2022; Universal Sets
• 5. Empty Sets &#x2022; A set that contains no members is called the empty set or null set . &#x2022; For example, the set of the months of a year that have fewer than 15 days has no member .Therefore ,it is the empty set. The empty set is written as { } or &#xF0C6;.
• 6. Finite Sets &#x2022; A set is finite if it consists of a definite number of different elements ,i.e., if in counting the different members of the set, the counting process can come to an end. &#x2022; For example, if W be the set of people living in a town, then W is finite.
• 7. Infinite Sets &#x2022; An infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. Some examples are: &#x2022; The set of all integers, {..., -1, 0, 1, 2, ...}, is a count ably infinite set;
• 8. Equal Sets &#x2022; Equal sets are sets which have the same members. Or Two sets a and b are said to be equal if they have the same no of elements. &#x2022; For example, if P ={1,2,3},Q={2,1,3},R={3,2,1} then P=Q=R.
• 9. Subsets &#x2022; Sets which are the part of another set are called subsets of the original set. &#x2022; For example, if A={1,2,3,4} and B ={1,2} then B is a subset of A it is represented by &#xF0CD;.
• 10. Power Sets&#x2022; If &#x2018;A&#x2019; is any set then one set of all are subset of set &#x2018;A&#x2019; that it is called a power set. &#x2022; Example- If S is the set {x, y, z}, then the subsets of S are: &#x2022; {} (also denoted , the empty set) &#x2022; {x} &#x2022; {y} &#x2022; {z} &#x2022; {x, y} &#x2022; {x, z} &#x2022; {y, z} &#x2022; {x, y, z} &#x2022; and hence the power set of S is {{}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}.
• 11. Universal Sets &#x2022; A universal set is a set which contains all objects, including itself. Or &#x2022; In a group of sets if all the sets are the subset of a particular bigger set then that bigger set then that bigger set is called the universal set. &#x2022; Example- A={12345678} B={1357} C={2468} D={2367} Here A is universal set and is denoted by
• 12. Operation Of Sets &#x2022; Union of sets &#x2022; Intersection of sets &#x2022; Compliments of sets
• 13. Union &#x2022; 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. &#x2022; Using set-builder notation, A U B = {x : x is a member of A or X is a member of B}
• 14. Intersection &#x2022; Intersection are written as A &#x2229; B, is the set of elements that are in A and B. &#x2022; Using set-builder notation, it would look like: A &#x2229; B = {x : x is a member of A and x is a member of B}.
• 15. Complements &#x2022; 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. &#x2022; Notation A&#x2019; ={1,2,3,4,5} A={1,2,3} A&#x2019;={2,4}
• 16. Some Other Sets &#x2022; Disjoint &#x2013; If A &#x2229; B = 0, then A and B are disjoint. &#x2022; Difference: B &#x2013; A; all the elements in B but not in A &#x2022; Equivalent sets &#x2013; two sets are equivalent if n(A) = n(B).
• 17. Venn Diagrams &#x2022; Venn diagrams are named after a English logician, John Venn. &#x2022; It is a method of visualizing sets using various shapes. &#x2022; These diagrams consist of rectangles and circles.