My Math Forum Injective relation

 Algebra Pre-Algebra and Basic Algebra Math Forum

 September 24th, 2017, 01:24 AM #1 Member   Joined: Sep 2014 From: Morocco Posts: 36 Thanks: 0 Injective relation Hello, I'm trying to work on the following: Let A be a subset of a set E. F is the relation that associates each X of P(E) with the symmetric difference of A and X. Show that F is injective. My idea has been to use the definition of an injective relation to show that for X and X' in P(E), if F(X) = F(X') then X = X'. Knowing that these two sets are equal if and only if their indicator functions are equal, I found a general formula for the indicator function of a symmetric difference, so that I can use it here. But I'm stuck.
September 24th, 2017, 10:15 AM   #2
Senior Member

Joined: Aug 2012

Posts: 1,956
Thanks: 547

Quote:
 Originally Posted by Mifarni14 My idea has been to use the definition of an injective relation to show that for X and X' in P(E), if F(X) = F(X') then X = X'.
Right, that's the definition of injective so that's the way to get started.

Quote:
 Originally Posted by Mifarni14 Knowing that these two sets are equal if and only if their indicator functions are equal, I found a general formula for the indicator function of a symmetric difference, so that I can use it here.
That sounds overly complicated. Does your formula work in the infinite case?

It's not hard to show that $A \bigtriangleup X$ and $A \bigtriangleup X'$ are different if $X \neq X'$. That's the way to go here.

Last edited by Maschke; September 24th, 2017 at 10:18 AM.

 Tags injective, relation

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post ach4124 Calculus 2 March 27th, 2015 05:37 PM uniquegel Algebra 4 September 8th, 2014 04:18 PM zaff9 Abstract Algebra 6 January 22nd, 2013 08:21 PM Zilee Applied Math 3 October 2nd, 2012 08:07 PM problem Calculus 0 October 1st, 2010 04:54 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top