R help - Feb 2013 - questions hash functions

Hello R, could you explain to me how to resolve this question:

If this is a matrix:

Element S1 S2 S3 S4
     0        0    1  0    1
     1        0    1  0    0
     2        1    0  0    1
     3        0    0  1    0
     4        0    0  1    1
     5        1    0  0    0


1.  How is possible to ompute the minhash signature for each column if
we use the following
three hash functions: h1(x) = 2x + 1 mod 6; h2(x) = 3x + 2 mod 6;
h3(x) = 5x + 2 mod 6.

2. Which of these hash functions are true permutations?

3.How close are the estimated Jaccard similarities for the six pairs of columns
to the true Jaccard similarities?

Thank you!

Tania

I cannot imagine why you think this is the appropriate place to pose such a
question. It certainly has nothing to do with R (which would be appropriate),
and it does look like homework (which is identified as NOT appropriate in the
Posting Guide for this mailing list).
---------------------------------------------------------------------------
Jeff Newmiller                        The     .....       .....  Go Live...
DCN:<jdnewmil at dcn.davis.ca.us>        Basics: ##.#.       ##.#.  Live
Go...
                                      Live:   OO#.. Dead: OO#..  Playing
Research Engineer (Solar/Batteries            O.O#.       #.O#.  with
/Software/Embedded Controllers)               .OO#.       .OO#.  rocks...1k
--------------------------------------------------------------------------- 
Sent from my phone. Please excuse my brevity.

"Tania Pati?o" <taniuxpc at gmail.com> wrote:
>Hello R, could you explain to me how to resolve this question:
>
>If this is a matrix:
>
>Element S1 S2 S3 S4
>     0        0    1  0    1
>     1        0    1  0    0
>     2        1    0  0    1
>     3        0    0  1    0
>     4        0    0  1    1
>     5        1    0  0    0
>
>
>1.  How is possible to ompute the minhash signature for each column if
>we use the following
>three hash functions: h1(x) = 2x + 1 mod 6; h2(x) = 3x + 2 mod 6;
>h3(x) = 5x + 2 mod 6.
>
>2. Which of these hash functions are true permutations?
>
>3.How close are the estimated Jaccard similarities for the six pairs of
>columns
>to the true Jaccard similarities?
>
>Thank you!
>
>Tania
>
>______________________________________________
>R-help at r-project.org mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide
>http://www.R-project.org/posting-guide.html
>and provide commented, minimal, self-contained, reproducible code.