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 September 24th, 2017, 01:24 AM #1 Member   Joined: Sep 2014 From: Morocco Posts: 43 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
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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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded 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

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