Set Theory and Operation

Set theory, a branch of mathematics, deals with the properties of well-defined collections of objects that may or may not have mathematical properties, such as numbers or functions.

SET THEORY

Set theory, a branch of mathematics that deals with the properties of well-defined collections of objects that may or may not have mathematical properties.

Set theory, as an independent mathematical discipline, began with the work of Georg Cantor. Some people may say that set theory was born at the end of 1873, when he made an amazing discovery that a linear continuum, that is, a real line, is uncountable, which means that its points cannot be calculated by natural numbers.

Therefore, even if both the set of natural numbers and the set of real numbers are infinite, there are more real numbers than natural numbers, which opens the door to investigating the different sizes of infinity.

Types of sets and set operations

(a) Algebraic set notation

e.g

. (i) P = {x:x is prime number less than 25}

P : Interpreted as prime numbers from 2 – 23

P = {2, 3, 5, 7, 11, 13, 17, 19, 23}

(ii) D = {X:XZ5 X 14}

It is interpreted as D is a set of X such that X is an integer and lies between 5 are 14 both inclusive i.e. X is greater or equal to 5, X less or equal to 14

D = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

(b) aX :- a is an element of X

P Q : P is not an element of Q

n(x): number of element in X

or : the universal set

or { }: the null or empty set

A¹ The complement of A

B B B is a subject of A

A⊃ B A is a super set of B

∪ Union

∩ Intersection