Category: Discrete structure

Group

Group A non-empty set G of some elements (a, b, c, etc.), with one or more operations is known as a group. A set needed to be satisfied following properties to become a group: 1) Closure Property:a.b ∈ G , ∀ a, b ∈ G 2) Associative Property:(a . b) . c = a . […]

Algebraic structure

Algebraic Structures G -> a non-empty set. G with one or more binary operations is known as algebraic structures. For examples 1) (G, ) , where ‘’ is an binary operation on Set/Group ‘G’. Than (G,*) is an algebraic group. 2) (N, +), where ‘+’ is an binary operation on Set/Group ‘N’,set of natural numbers. […]

Binary operations

SET Set is a collection of definite well defined objects. Set is denoted by capital letter. For example: A = {a, b, c, d, e} BINARY OPERATIONS ON A SET Let, G à a non-empty set GXG = {(a ,b): a ∈ G, b ∈ G }. Above line is read as: G cross G equal to (a, b) such that ‘a’ […]

Relation

Prob. Let A,B,C be any three sets, then prove that-AX(B∩C) = (AXB) ∩ (AXC) Solution:(x,y) ∈ Ax(B∩C)x∈A and (y∈(B∩C))x∈A and (y∈B and y∈C)(x∈A and y∈B) and (x∈A and y∈C)(x,y) ∈ (A x B) and (x,y) ∈(A x C) // by Cartesian Product. (x,y) ∈ (AxB)∩(AxC) Prob. Prove that-A∩(B∪C) = (A∩B) ∪ (A∩C) Solution:Let x ∈ […]

Mathematical induction

Mathematical induction is a unique and special way to prove the things, in only two steps. Step 1. Show that it is true for n = 1.Step 2. Show that if n = k is true then n = k+1 is also true. For example:Prob. By principal of mathematical induction prove that11n+2 + 122n+1 is divisible by 133, n ∈ […]

SET

A set is a collection of definite well defined objects.A set is a collection of objects which are distinct from each other. A set is usually denoted by capital letter, i.e, A, B, S, T, G etc.A set elements are denoted by small letter, i.e, a, b, s, t etc. CONSTRUCTION OF SET: In construction […]

Net 34

CBSE NET December 2015 PAPER II Q.Which of the following property/ies a Group G must hold, in order to be an Abelian group? (a) The distributive property (b) The commutative property (c) The symmetric property Codes: (A) (a) and (b) (B) (b) and (c) (C) (a) only (D) (b) only Ans :- (D) Explanation:- A […]