[MUG] Set And List Problem

[MUG] Re: Set And List Problem
Author: Maple User Group    Posted: Fri, 1 Nov 2002 10:23:57 -0500 (
>> From: Maple User Group "maple_gr" | >> From: "UKC Account" "crp3" | I have this question on an assignment to do with sets and lists. It | reads: | 'Let A be the set {1,2,3,...,25}. Create the set, B, of all subsets of A | of size 2 containging at least one odd integer. Determine the number of | elements in B.' -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Tue, 29 Oct 2002 14:30:54 -0500 From: Bill Bauldry "BauldryWC" Subject: Set And List Problem To: "maple-list" You could try something like: > with(combinat): Warning, the protected name Chi has been redefined and unprotected > OddInt := x -> convert(map(type,x, odd), `or`); > Size := n -> (x -> evalb(nops(x)=n)); OddInt := x -> convert(map(type, x, odd), `or`) Size := n -> x -> evalb(nops(x) = n) > P5 := powerset({$1..5}); P5 := {{}, {1, 4, 5}, {1, 2, 4, 5}, {2, 4, 5}, {2, 3, 4, 5}, {3, 4, 5}, {1, 3, 4, 5}, {1, 2, 3, 4, 5}, {4, 5}, {3, 5}, {2, 3, 5}, {1, 2, 3, 5}, {1, 3, 5}, {1, 5}, {2, 5}, {1, 2, 5}, {1}, {5}, {2}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}, {4}, {1, 4}, {2, 4}, {1, 2, 4}, {3, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}} > TheOdds := select(OddInt, P5); > TheEvens := remove(OddInt, P5); TheOdds := {{1, 4, 5}, {1, 2, 4, 5}, {2, 4, 5}, {2, 3, 4, 5}, {3, 4, 5}, {1, 3, 4, 5}, {1, 2, 3, 4, 5}, {4, 5}, {3, 5}, {2, 3, 5}, {1, 2, 3, 5}, {1, 3, 5}, {1, 5}, {2, 5}, {1, 2, 5}, {1}, {5}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}, {1, 4}, {1, 2, 4}, {3, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}} TheEvens := {{}, {2}, {4}, {2, 4}} > Odd2 := select(Size(2), TheOdds); > Even2 := select(Size(2), TheEvens); Odd2 := {{4, 5}, {3, 5}, {1, 5}, {2, 5}, {1, 2}, {1, 3}, {2, 3}, {1, 4}, {3, 4}} Even2 := {{2, 4}} Regards, Bill ______________________________________ Wm C Bauldry, PhD Professor and Chairperson Department of Mathematical Sciences Appalachian State University 121 Bodenheimer Dr Boone, NC 28608-2092 _____________________ phone: (828) 262-3050 fax: (828) 265-8617 "mailto:BauldryWC" http://www.mathsci.appstate.edu/~wmcb/ ______________________________________ -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Tue, 29 Oct 2002 15:09:48 -0500 (EST) From: Carl Devore "devore" To: "maple-list" Subject: Set And List Problem A:= {$1..25}; B:= combinat[choose](A,2) minus combinat[choose]({2*k $ k= 1..12}, 2); The answer is 234, not 244: 25*24/2 - 12*11/2; -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Tue, 29 Oct 2002 17:37:14 -0600 From: "ayon" To: "maple-list" Subject: Set And List Problem I'm not secure if the next approaches are correct solutions to your question, but in both cases the number of combinations appears to be 234: > A:={$1..25}; C:=select( type, A, odd ); A := {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25} C := {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25} > B:={seq( seq( {C[i],j}, j=A minus C[1..i] ), i=1..nops(C) )}: > nops(B); 234 The other approach is: > {seq( seq( {i,j}, j=A minus {i} ), i=A )}: B:=select( hastype, %, odd ): nops(B); 234 Eloy Ayon-Beato Physics Department CINVESTAV-IPN ------------------------------------------------- This mail sent through IMP: http://horde.org/imp/ -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Tue, 29 Oct 2002 00:48:41 -0400 From: C W "sylvester7" To: "maple-list" "crp3" Subject: Set And List Problem Try this : R:=rand(25): FS:=(proc(lO,lE) local vO,vE;{op(combinat[choose](lO,2)),seq(seq({vO,vE},vO=lO),vE=lE)} end)@(proc(S) (select,remove)(type,S,odd) end): S:={seq(R(),i=1..12)};SS:=FS(S);nops(SS); Chris -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: "Daniel Willard" "willardd" To: "maple-list" Subject: Set And List Problem Date: Wed, 30 Oct 2002 10:06:48 -0500 In Abramowitz and Stegun "Handbook of Mathematical Functions" (Published by the National Institute for Science and Technology - ex NBS) you will find a discussion of functions very like the ones you want.

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