The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
+16 votes

The set {1,2,3,5,7,8,9} under multiplication modulo 10 is not a group. Given below are four possible reasons. Which one of them is false?

  1. It is not closed
  2. 2 does not have an inverse
  3. 3 does not have an inverse
  4. 8 does not have an inverse
asked in Set Theory & Algebra by Active (3.7k points) | 1.5k views
8*7=56%10=6..not in the set it is not closed ...why it cant be the anssssss
@asu Bhai question is bit tricky asked

they are asking which one is false.

Here 3 having inverse which is 7 .bcz 3*7=21mod10=1 //1 is identity element

but they are telling 3 does not have an inverse. So false.So C is Ans.

(8 does not have an inverse.This statement is true..but they asked for false. so it cant be ans)

3 Answers

+19 votes
Best answer
Answer: C

3 has an inverse, which is 7. As, 3*7 mod 10 = 1.
answered by Boss (34.1k points)
selected by
The given relation is not closed also, 2*8 mod 10 = 6 which doesn't belong to the set. Can it be a reason for it not being a group?
yes , it is one of the reasons.
+2 votes
Ans C.
answered by Boss (13.5k points)
In the question it is asked which is false. and given that it's not a group. As we can see 3 have an inverse which is 7 therefore this statement is false
+1 vote
Hi , please correct me if I am wrong. The set is {1,2,3,5,7,8,9} and we need to do multiplication modulo 10.  So, 2 (multiplication modulo 10 ) 2 = 4 , which is not in the set. That means , it is not closed.

Please correct me , if I am wrong .
answered by Active (4.1k points)

You're right 0,4,6 are missing ; so for every n mod 10 = {0,4,6} this set is definitely not closed.

But trick is it is not closed is not false reason ; it's True.

Ohh yeah.. sorry didn't see the question properly. my bad :( . Yes , it is true. thanks
Question is asking which of the statement is not FALSE.. Yes it is not closed is a True statement.

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

35,500 questions
42,768 answers
42,151 users