introduction to set theory

In any application of the theory of sets, the members of all sets under consideration usually belong to some fixed large set called the universal set. Usually we denote the universal set by the letter..

Union of sets - If two sets are given, a set can be formed by using all the elements of the two sets. Such a collection is called the union of the given sets..

A set can be formed by using all the common elements of two given sets. Such a collection is called the intersection of the given sets..

There are two methods of representing a set. (i) Roster Method (ii) Set builder fo..

Capital letters are usually used to denote or represent a set. viz., A, B, C, D, . . . . The elements of sets are usually represented by lower case letters. viz., a, b, c, x, y, . ..

Two sets A and B are said to be equal if and only if they contain the same elements i.e. if every element of A is in B and every element of B is in A. We denote the equality by A = ..

Let U be a universal set, A be any subset of U, then the elements of U which are not in A i.e., U - A is the complement of A w.r.t. U is written as A' = U - A = A c ..

Example: - In a class of 80 boys, there are 60 boys who play rugby and 35 play tennis. Use Venn diagrams to show how many boys play both the games? How many play rugby only and how many play tennis onl..

Introduction - If m is a positive integer, a x a x a . m times is written as a m . a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent". When the power or index is a fraction say then and it is a surd of o..

Introduction - Let us consider the marks obtained by four students in Physics, Chemistry and Biology for the first unit test. We have represented the data in rows and columns. (i) Rows show the marks obtained by each student. (ii) The columns show the marks in Physics, Chemistry, Biology ..