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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  
Senior Member Joined: Aug 2012 Posts: 2,357 Thanks: 740  Quote:
Quote:
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.  

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