The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
0 votes

Consider the following binary operations on Z. which of the following operations form a group
i. x*y = x+y+2   for x,y ∈ Z.
ii. x*y = xy + 2x + 2y +2 for x,y ∈ Z
iii. x*y=x2y2 for x,y ∈ Z

asked in Set Theory & Algebra by Veteran (16.8k points) | 105 views

1 Answer

+2 votes
Best answer

i. * closed operation, x*y belongs to Z
ii. Associative
iii.    x*e = x
        x + e + 2 = x
        e = -2      // identity element exists
iv.  x*y=e   
      x+y+2 = -2
           y = (-4 -x)    inverse exist
v. Commutative

Hence statement 1 is Abelian Group!


Statement 2:  Not Associative

Statement 3. 
x*y=x2yfor x,y ∈ Z   not associative not even semi group

answered by Veteran (16.8k points)
edited by
thank you @sushant for the correction!

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

28,982 questions
36,818 answers
34,706 users