Answer to Question #259701 in Discrete Mathematics for tushar

Question #259701

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 (𝑅βˆͺ S)


1
Expert's answer
2021-11-02T15:36:25-0400

1.

Rc=AΓ—Aβˆ’RR^c=A\times A-R

M(Rc)=(0110111110111001)M(R^c)=\begin{pmatrix} 0 & 1&1&0 \\ 1 & 1&1&1\\ 1 & 0&1&1\\ 1 & 0&0&1 \end{pmatrix}


2.

Sβ€Ύ=AΓ—Aβˆ’S\overline{S}=A\times A-S

M(Sβ€Ύ)=(0011101111011010)M(\overline{S})=\begin{pmatrix} 0 & 0&1&1 \\ 1 & 0&1&1\\ 1 & 1&0&1\\ 1 & 0&1&0 \end{pmatrix}


3.

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

M(RβˆͺS)=(1101010001100111)M(R\cup S)=\begin{pmatrix} 1 & 1&0&1 \\ 0 & 1&0&0\\ 0 & 1&1&0\\ 0 & 1&1&1 \end{pmatrix}


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