Question

Let A= {1, 2, 3, 4}, and let R And S be the relations on A As follow: R = {(1,1),(1, 4),(3,2),(4,2),(4,3)} S = { (1,1),(1,2),(2,2),(3,3),(4,2),(4,4)) Then find out: 1. M𝑅𝑐 2. 𝑀𝑠̅ 3. M (𝑅∪ S)

Answer 1

1.

$R^c=A\times A-R$

$M(R^c)=\begin{pmatrix} 0 & 1&1&0 \\ 1 & 1&1&1\\ 1 & 0&1&1\\ 1 & 0&0&1 \end{pmatrix}$

2.

$\overline{S}=A\times A-S$

$M(\overline{S})=\begin{pmatrix} 0 & 0&1&1 \\ 1 & 0&1&1\\ 1 & 1&0&1\\ 1 & 0&1&0 \end{pmatrix}$

3.

$R\cup S=\{ (1,1),(1,2),(1,4),(2,2),(3,2),(3,3),(4,2),(4,3),(4,4)\}$

$M(R\cup S)=\begin{pmatrix} 1 & 1&0&1 \\ 0 & 1&0&0\\ 0 & 1&1&0\\ 0 & 1&1&1 \end{pmatrix}$