Ganitagya Gyanam

 Introduction of relations: when the word relation comes to our mind then we discuss the relations with our family, friends, and colleagues but here we are going to discuss the relation in mathematics. We have to understand that relations in sets are very important and we use these relations in our daily life.  The only way to learn mathematics is to do mathematics - Paul Halmos Introduction In our daily life, we come across many patterns that characterize relations such as brother and sister, father and son, teacher and student. In mathematics also, we come across many relations such as number `m` is less than number `n`, line `l` is parallel to line `m`, set `A` is a subset of set `B`. In all these, we notice that a relation involves pairs of objects in certain order. Cartesian Product Given two non-empty sets `S` and `T`. The Cartesian product `S \times T` is the set of all ordered pairs of elements from `S` and `T`, such that `S \times T=\{(s, t): s \in S, t \in T\}...

 Principle of Inclusion-Exclusion: maximum time a question arises in students mind that where we can use this concept of the Inclusion-Exclusion principle. In our daily life, we use this concept of the Inclusion-Exclusion principle. Let us see how we can use this concept by taking few examples and first understand the principle. Are you ready to start?

Mathematics is the most beautiful creation of the human spirit-Stefan Banach  Venn diagrams the relations between sets can be illustrated by certain diagrams. Venn Diagrams are very important in all aspects. It provides an understanding of the concept visually.  Under this article understand the concept of union, intersection, the difference of two sets and symmetry of two sets, and compliment of a set. Also, we discuss the algebraic laws on sets and solve a few examples to understand all these concepts. So, are you ready to understand the concept of the Venn diagram? The relationships between sets can be represented by means of diagrams which are known as Venn diagrams. These diagrams consist of rectangles and closed curves usually circles. The universal set is represented usually by a rectangle and its subsets by circles.  Operations on Sets We will now define certain operations on sets and examine their properties. Henceforth, we will refer all our sets as subsets o...