Recursive Equations

[Guest]

R= { (1,1), (1,2), (1,4), (2,2), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,4), (5,1), (5,3) }

a- Show the MR matrix .
b- S= { (1,2), (1,3), (1,4), (2,2), (2,3), (2,5), (3,1), (3,2), (3,5), (4,2), (4,4), (5,1), (5,2) }

MS o R = ?

[Guest]

What does it mean MR matrix?

[Guest]

MR MATRIX
M is matrix of R

[Guest]

You can find MR by using a 5*5 matrix. each row corresponding to one element in [tex]A= \lbrace 1,2,3,4,5 \rbrace[/tex], each column corresponding to each of the elements of [tex]B = \lbrace 1,2,3,4,5 \rbrace[/tex] . Then the [tex]m_{i,j}[/tex] entry will be a 1 if [tex](a_i,b_j)[/tex] is one pair in the set of relations, ad 0 otherwise.
Therefore

[tex]MR =\begin{pmatrix}
1 & 1 & 0 & 1 & 0 \\
0 & 1 & 0 & 1 & 1 \\
1 & 1 & 1 & 1 & 0 \\
0 & 0 & 0 & 1 & 0 \\
1 & 0 & 1 & 0 & 0 \\
\end{pmatrix}[/tex]

I think you want [tex]M(S o R)[/tex]. First notice that:
[tex]S o R = \lbrace (1,2),(1,3),(1,4),(1,2),(1,3),(1,5),(1,2),(1,4),(2,2),(2,3),(2,5),[/tex][tex](2,2),(2,4),(2,1),(2,2),(3,2),(3,3),(3,4),(3,2),(3,3),(3,1),(3,2),(3,5),(3,2),(3,4),(4,2)[/tex][tex],(4,4),(5,2),(5,3),(5,4),(5,1),(5,2),(5,5) \rbrace[/tex]
[tex]= \lbrace (1,2),(1,3),(1,4),(1,5),(2,1),(2,2),(2,3),(2,4),[/tex][tex](2,5),(3,1),(3,2),(3,3),(3,4),(3,5),(4,2),(4,4),(5,1),(5,2),(5,3),(5,4),(5,5) \rbrace[/tex]

Now
[tex]M(S o R ) =\begin{pmatrix}
1 & 1 & 1 & 1 & 1 \\
1 & 1 & 1 & 1 & 1 \\
1 & 1 & 1 & 1 & 1 \\
0 & 1 & 0 & 1 & 0 \\
1 & 1 & 1 & 1 & 1 \\
\end{pmatrix}[/tex]

[tex]

[Guest]

MS=?
MS o R =?