Re: Or in a Select question

• To: mathgroup at smc.vnet.net
• Subject: [mg67107] Re: [mg67066] Or in a Select question
• From: ggroup at sarj.ca
• Date: Fri, 9 Jun 2006 01:09:07 -0400 (EDT)
• References: <200606080854.EAA12393@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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]\",
> ButtonStyle->\"RefGuideLinkText \", \ ButtonFrame->None,
> ButtonData:>\"General::partd\"]\)" From In[104]:= Part::"partd":"Part
> specification \!\(v \[LeftDoubleBracket] 2 \ \[RightDoubleBracket]\)
> is longer than depth of object. \ \!\(\*ButtonBox[\"More\[Ellipsis]\",
> ButtonStyle->\"RefGuideLinkText \", \ ButtonFrame->None,
> 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)

```

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