Re: Or in a Select question

• To: mathgroup at smc.vnet.net
• Subject: [mg67108] Re: [mg67066] Or in a Select question
• From: János <janos.lobb at yale.edu>
• Date: Fri, 9 Jun 2006 01:09:14 -0400 (EDT)
• References: <200606080854.EAA12393@smc.vnet.net> <20060608195255.M47050@sarj.ca>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi ggroup,

Some times ago I had to study mathematical logic, but looks like in
my case that knowledge was very much concentrated close to the scalp,
so when the hair started to fall out so did the logic grabbing to it
from underneath :)

I still would like to know why did I get the error message below for
Cases when I replaced the === with the =!=

That was my original reason to ask the list :)

Thanks a lot,

János

On Jun 8, 2006, at 3:52 PM, ggroup at sarj.ca wrote:

> You are missing a basic identity in logic:
>
> Assume A & B are True/False statements, then
>
> !A || !B  == !( A && B )
> !A && !B  == !( A || B )
>
> As far as I can tell, the logic you've used in the first example is:
> First Pair don't match OR Second Pair don't match
>
> Symbolically,
> A = First Pair match
> B = Second Pair match
> !A || !B
>
> What you want is:
> First Pair don't match AND Second Pair don't match
>
> Symbolically,
> A = First Pair match
> B = Second Pair Match
> !A && !B
>
> Depending on how you like to think about these things, it may be
> more obvious
> to write the equivalent of the last example:
> Neither the first nor the second pair match
>
> Symbolically
> A = First pair match
> B = Second pair match
> !(A||B)
>
> Hope that helps!
>
>
> On Thu, 8 Jun 2006 04:54:07 -0400 (EDT), János wrote
>> Hi,
>>
>> I have a list
>>
>> lst={a,b,c}
>>
>> I make another list from it the following way:
>>
>> In[2]:=
>> pp = Partition[Tuples[lst,
>>      2], 2, 1]
>> Out[2]=
>> {{{a, a}, {a, b}},
>>    {{a, b}, {a, c}},
>>    {{a, c}, {b, a}},
>>    {{b, a}, {b, b}},
>>    {{b, b}, {b, c}},
>>    {{b, c}, {c, a}},
>>    {{c, a}, {c, b}},
>>    {{c, b}, {c, c}}}
>>
>>  From here I would like to select all the elements whose sublists
>> contain only different elements.  So my "logical" selection was:
>>
>> In[54]:=
>> Select[pp,
>>    #1[[1,1]] =!= #1[[1,2]] ||
>>      #1[[2,1]] =!= #1[[2,
>>        2]] & ]
>> Out[54]=
>> {{{a, a}, {a, b}},
>>    {{a, b}, {a, c}},
>>    {{a, c}, {b, a}},
>>    {{b, a}, {b, b}},
>>    {{b, b}, {b, c}},
>>    {{b, c}, {c, a}},
>>    {{c, a}, {c, b}},
>>    {{c, b}, {c, c}}}
>>
>> Well, that did not do any damage to the list.  After some time I came
>> up with this one:
>>
>> In[49]:=
>> Complement[pp, Select[pp,
>>     Xor[#1[[1,1]] =!=
>>        #1[[1,2]],
>>       #1[[2,1]] =!= #1[[2,
>>         2]]] & ]]
>> Out[49]=
>> {{{a, b}, {a, c}},
>>    {{a, c}, {b, a}},
>>    {{b, c}, {c, a}},
>>    {{c, a}, {c, b}}}
>>
>> That looks OK, but also looks too complicated.  Why my "logical" one
>> does not work here?
>>
>> Interestingly if I just use either the left or right side of the Or,
>> that partial select is working.  For example:
>>
>> In[65]:=
>> Select[pp, #1[[1,1]] =!=
>>      #1[[1,2]] & ]
>> Out[65]=
>> {{{a, b}, {a, c}},
>>    {{a, c}, {b, a}},
>>    {{b, a}, {b, b}},
>>    {{b, c}, {c, a}},
>>    {{c, a}, {c, b}},
>>    {{c, b}, {c, c}}}
>>
>> Now if I try with Cases and conditional pattern matching then the
>> selection for sublists with identical elements works:
>>
>> In[98]:=
>> Cases[pp, {u_, v_} /;
>>     u[[1]] === u[[2]] ||
>>      v[[1]] === v[[2]]]
>> Out[98]=
>> {{{a, a}, {a, b}},
>>    {{b, a}, {b, b}},
>>    {{b, b}, {b, c}},
>>    {{c, b}, {c, c}}}
>>
>> If I change here the === to =!=, then I do not get again that I
>> expect:
>>
>> In[103]:=
>> Cases[pp,
>>    (({u_, v_} /; u[[1]]) =!=
>>       u[[2]] || v[[1]]) =!=
>>     v[[2]]]
>>  From In[103]:=
>> \!\(\*
>>    RowBox[{\(Part::"partd"\),
>>      ":", "\<\"Part specification \\!\\(u \[LeftDoubleBracket] 2 \
>> \[RightDoubleBracket]\\) is longer than depth of object. \
>> \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\
>> \\\", ButtonFrame->None, ButtonData:>\\\"General::partd\\\"]\\)
>> \"\>"}]\) From In[103]:= \!\(\*   RowBox[{\(Part::"partd"\),     ":",
>>  "\<\"Part specification \\!\\(v \[LeftDoubleBracket] 2 \
>> \[RightDoubleBracket]\\) is longer than depth of object. \
>> \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\
>> \\\", ButtonFrame->None, ButtonData:>\\\"General::partd\\\"]\\)
>> \"\>"}]\) Out[103]= {} From In[104]:= Part::"partd":"Part
>> specification \!\(u \[LeftDoubleBracket] 2 \ \[RightDoubleBracket]\)
>> is longer than depth of object. \ \!\(\*ButtonBox[\"More\[Ellipsis]
>> \",
>> ButtonData:>\"General::partd\"]\)" From In[104]:= Part::"partd":"Part
>> specification \!\(v \[LeftDoubleBracket] 2 \ \[RightDoubleBracket]\)
>> is longer than depth of object. \ \!\(\*ButtonBox[\"More\[Ellipsis]
>> \",
>> ButtonData:>\"General::partd\"]\)"
>>
>> if I change =!= to only != then I still do not get that I expect:
>>
>> In[108]:=
>> Cases[pp, {u_, v_} /;
>>     u[[1]] != u[[2]] ||
>>      v[[1]] != v[[2]]]
>> Out[108]=
>> {}
>>
>> Obviously I am not GETting something here :)
>>
>>
>> János
>> P.S.  It is 5.1 on OSX 10.4.6.  I know that Or evaluates in a non-
>> traditional way and looked the Appendix - that is how I ended up with
>> Xor.
>>
>> ----------------------------------------------
>> Trying to argue with a politician is like lifting up the head of a
>> corpse.
>> (S. Lem: His Master Voice)
>
>
>

----------------------------------------------
Trying to argue with a politician is like lifting up the head of a
corpse.
(S. Lem: His Master Voice)

```

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