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MathGroup Archive 2005

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Re: operators for relations in sets

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60346] Re: [mg60338] operators for relations in sets
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Wed, 14 Sep 2005 03:27:14 -0400 (EDT)
  • References: <200509131007.GAA09833@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 13 Sep 2005, at 19:07, hawkmoon269 wrote:

> I'm having some difficulty understanding the behaviour of the  
> operators
> for relations in sets in Mathematica.  For instance,
>
> TrueQ[{1}\[SubsetEqual]{1}]
>
> returns
>
> False
>
> I'm not getting what's going on here...
>
> h
>
>

First of all, \[SubsetEqual] is not defined in Mathematica. You can  
define your own function SubsetEqual as:

SubsetEqual[A_List, B_List] := Intersection[A, B] == A

so that


SubsetEqual[{1},{1,2}]

True

etc. If you really want with the help of the Notation package you can  
make the infix form A\[SubsetEqual]B equivalent to Subsetequal[A,B]  
(although i would not bother).

As for TrueQ, it serves a completely different purpose. Note that  
TrueQ always gives False whenever something is not explicitly true,  
for example


TrueQ[Sin[x]^2+Cos[x]^2==1]

False

although


TrueQ[Simplify[Sin[x]^2+Cos[x]^2==1]]

True

TrueQ has its uses but your example is not one  of them!.

Andrzej Kozlowski


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