[R] questions hash functions

[Tania Patiño]

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