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. Mπ π 2. ππ Μ 3. M (π βͺ S)
1.
Rc=AΓAβRR^c=A\times A-RRc=AΓAβR
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}M(Rc)=βββ0111β1100β1110β0111ββ ββ
2.
SβΎ=AΓAβS\overline{S}=A\times A-SS=AΓAβS
M(SβΎ)=(0011101111011010)M(\overline{S})=\begin{pmatrix} 0 & 0&1&1 \\ 1 & 0&1&1\\ 1 & 1&0&1\\ 1 & 0&1&0 \end{pmatrix}M(S)=βββ0111β0010β1101β1110ββ ββ
3.
RβͺS={(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)\}RβͺS={(1,1),(1,2),(1,4),(2,2),(3,2),(3,3),(4,2),(4,3),(4,4)}
M(RβͺS)=(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}M(RβͺS)=βββ1000β1111β0011β1001ββ ββ
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments
Leave a comment