# Mathematics set theory presentation.

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### Mathematics set theory presentation.

• 2. SET THEORY CONTENTS • 1. Meaning and definition. 2. Representation of a set. 3. Set notation. 4. Types and kinds of set. 5. Sub-set and Universal set. 6.Union OF SET 7. Intersection of set. 8. DE-MORGAN’S LAW.
• 3. MEANING AND DEFINITATION • The concept of set was introduce in the end of 19th century by German mathematician GEORGE CANTER (1845-1918) • A set a structure ,representing an unordered collection (group , plurality) of zero or more distinct(different) objects. • The objects that makes up a set is called member or objects of the set. • Set theory deals with operations between ,relations among ,and statements about sets.
• 4. REORESENTATION OF SET A set can be represented by two method (1). Tabular or Roster method = Under this method ,the element of a set are enumerated or listed within parentheses ( ), , , separated by commas (,) . (2). Builder method = Under this method , the element are indicated by description of their characteristics or properties .( x: x is a element of a set )
• 5. SET NOTATION • Normally set are denoted by capital letters of English alphabet like A,B,C,D,…..X,M ,Z .Example A=( 1,2,3,4,5,6). • If X is an element of a set A ,it is written as X is not equal to A and read as ‘X’ does not belongs to ‘A’ or ‘x’ is not an element of ‘A’ or ‘x’ is not in A. Example A= (1,2,3,4,) then 3 is = A But 2 is not = to a.
• 6. TYPES and KINDS OF SET • (a). Finite set = A set is said to be finite set if the number of elements in it is finite . example A= (Delhi , Kolkata) • (b). Infinite set = A set is said to be infinite set if the elements of the set are infinite or unlimited . Example A=(1,2,…..). • (c) Null set = A set is said to be null if no element belongs to it. Example =( ). • (d) singleton set = A set consisting of single element is called singleton set. Example =A(1). • (e) Disjoint set = if two set A and B have no element in common ,is said to be disjoint set. • Example = A(1,2,3,) B=(4,5,6,)
• 7. SUB -SET • If two set A and B are that each element of A is also an element of B , then set A is called a sub set of the set B. • EXAMPLE: A =(1,2,3,4,5,6,) • B= (4,5,6,) • IN THIS ‘A’IS NOT A SUB SET OF ‘ • ‘B’.
• 10. DE-MORGANS LAW’S • DE-MORGAN’S LAW are a pair of transformation rules that are both valid of inference. Its named after “Augustus De Morgan” a 19th century British mathematician.
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