# Discrete structure

## Prove that G={−1,1,i,−i} is a group under multiplication.

First need to show that G is indeed closed under the operation * we have 1∗1=1 where 1∈G we have −1∗−1=1 where 1∈G we have … Read more

## Prove the following by using the principle of mathematical induction for all n ∈ N, 1³ + 2³ + 3³ + … + n³ = [n (n + 1)/2]²

Prove the following by using the principle of mathematical induction for all n ∈ N1³ + 2³ + 3³ + … + n³ = [n … Read more

## Undirected Graph and Incident Matrix

Undirected Graph Incident Matrix E1 E2 E3 E4 E5 V1 1 0 0 1 0 V2 0 1 1 0 0 V3 1 1 … Read more

## if a*c = c*a and b*c = c*b, then (a*b)*c = c*(a*b)

Prob. Let (A, ) be a semigroup. Show that for a, b, c ∈ A, if ac = ca and bc = cb, then (ab)c … Read more

## Show that a*b=b*a

Prob. Let ({a, b}, * ) be a semigroup where aa =b. Show that- ab=b*a. Sol. Given ({a*b}, *) is a semigroup And a*a = … Read more

## Show that (…, -4, -3, -2, -1, 0, 1, 2, 3, 4,…} is group

Prob. Show that the set I of all integers (…, -4, -3, -2, -1, 0, 1, 2, 3, 4,…}. Is a group with respect to … Read more

## 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, ) , … Read more

## 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 … Read more