The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+11 votes
1.3k views

Consider the set $\Sigma^*$ of all strings over the alphabet $\Sigma = \{0, 1\}$. $\Sigma^*$ with the concatenation operator for strings

  1. does not form a group

  2. forms a non-commutative group

  3. does not have a right identity element

  4. forms a group if the empty string is removed from $\Sigma^*$

asked in Set Theory & Algebra by Veteran (69k points) | 1.3k views

1 Answer

+24 votes
Best answer
Identity element for concatenation is empty string $\epsilon$. Now, we cannot concatenate any string with a given string to get empty string $\implies$ there is no inverse for string concatenation. Only other 3 group properties -- closure, associative and existence of identity -- are satisfied and hence, ans should be (a).
answered by Loyal (2.8k points)
selected by
U are right
why not inverse?
Identity element for concatenation is empty string $\epsilon$. Now, we cannot concatenate any string with a given string to get empty string $\implies$ there is no inverse for string concatenation.
ok. similar to division by zero. not defined. illogical. doesnt make sense.

 

thanks.
think about concatinating  string with some any other string to get null string...you will not find any such string so there is no inverse thats it
difference between right identity and left identity element ?

There exists identity element e such that,

                1) a*e = a for all a belongs to set    (right identity)

                2) e*a = a for all a belongs to set     (left identity)

Is this correct ???
Can we say Commutative property also fails here?

@  Bhagirathi

your answer always crystal clear... :) it proves me very helpful..

of course Anil

$ab \neq ba$

$ab$ is string that start with a and end with b , and have length 2 while $ba$ is a string that starts with b and ends with a and have length 2 , clearly both are different strings.
Answer:

Related questions



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

33,687 questions
40,230 answers
114,268 comments
38,795 users