Date
Relatim.
Relatie au clied Catianuaducr
Ba, b,c}
AXB: PU,a),C,5)[1, c),
(a,a),(2,b), (3,)4
and B etug emty et, hn
RSAXB
AXB f,b), aeA and bE B
Aa2} and B:sl, 2,
R,*fCID, Ch3), (2,D2,2)
ulatiou
RCR
st hmax- AX&
Totalm= no
n0-
S, Aclationy
eemnta et
n: no- lements
3
|PDale:
age No:
Binay
erAand t
eloment
eond elemn
ARS= fo,1), Ca,2),Cha}
Page i0
Datr
Relaioy
R AB
dunstud by ARB
ExanLble
det A=
AXB: (x,D,z,D, (a,)ay2,y)
(a,), (z,,
RCAXB
’ R X
Smpoyton Tesms
Ca,b) eR,thenit ii natd hy aRB
ReAxB.
Page No:
Dale:
A1,2,3} B(2,?
R- fl2), CÉy).
Donia
The der fac ila,b)e R
the doman
Dem (R)
Tu deMa o a Relatieut
The aer§ bEB: Ca, b) eR e abne aeB
AXB =2,),(2,), (2,s), (3,4), (2,5), (4,5!
Domainf 2, 3, 4
Set Oeatous on Relatiou
Union
Ohtseotion R ond S:
(Rn
Complemant:
2
R= ARB,S= cRO
Rifca,x), z,), (4,)}
Ro ARB
S=
|Paqe No
Date
RUS
Matai Reveentalisu al a Relatibu
A:2,3,43
A=$L2,9,4
R:jh),U,), (,9, (2,3, (2,9,(34)}
Main kepuuntaliou
| 2 3
M 2
H
Ri a Rolatiou uam 4to B dcn thar aRb
Matix
A), 2,3, 4}
Bf,u, G,8,9 Y
R: fCi,D, ca,4), (3,a)}
2, 33
4,93
Rolato Mahs
46 q
3 89
Fate ho
Date
felatioe
0 Rejexiudelatiou -
Asulalou R ulexiue
elemen ae A, aRVa,ie
A fa, by
R,e fa, a), (b, b)} Rg >flb,b) (a,Ca)y
b) b.o)
Rz (a,a), (5, b), Ca,b)
’A2,3y
), (2,2), (9,3)y
Rs fCa,b), (b,a)y Sreutue
A=fl,2,s
Rysli), (2,2),(3,D,(i,3)} K1jlexuin
Rg: , ,(2,3), c2,1)) Sunle
Ra(3,), c4,s), (1,) s ne7tiwiie
hg 0,), (2,2),(3,3), (4,), (r,)y
lemnt atA,oaeCa,a) R
aymmaldi Relation CaRb ten bRa)
aynmut
eu
if
fatians
lune) aRb then b Ra. sf
R U,2, (2,D, (2,), C3,1)
Rs 022, (2,2), (2, )}
fL (2,2), (3,) tiu ymmaba
(some)
Puhneubs aRb nol bRC then aRce
3t folsuu thara selatin
hne exoh elemunte a,b, ce4 duch
aRb
Page Na
Dale
touúvalentr ielatiou
symmethie tranailiue.
diicble by
diuibl
Xuctagu 3-2-l, 0,1, 2,3-.}
elatou
aRb 213X9
bRa 16 X5
-3)
Dafe:
TAaniilut
aRb,bRC
tien aRc
Rz
3m
3t3
3(m+n)
Page Ho
Date
tantily klaica
Llenity uelatuou uche
Aelateel to
2
2
I,RS,D, (2,2), (3,3
Nist dcenti suelatiou ou dek A Daubles
Relation
Rellexiue Relatiou ’ A elatòu Ron sert
f (o, a) ER fo ale aet
A
et AA: l,2, 3}
elato
R:A 2
3
element Auoud de elated to
ulatd to
SU
Page tir
Dale
Mandoto
Re fC,) (9,2,3), C,D(0,)} Rifeeut
}0D, (2,2), C3,3) sdently Rejozu
ser A doublets
dementa
etue odued ban Cobti cna)
nod be ldentily
dlentity elaiou u uu
mat
R
Re fa),(2,2) (3,)?
Ri),(2,2), 3,5),4,y
RC,D, (,2) 332, c2,2)3
R u , ) (1,2),(2,2)}
R (,D(3,)3
(empty ulaligu
R-D, (2,2), (s,3
ymmtt Rolatia
ulale ou seA l,2,3 y called
4
1f (a,b) ER>,a) eR
A=1.2,3}
Idom
R3), C), (3,9, (2),(2.2 symabie
RX
uivae Relatiovv
)Ca, whe not uile ies
eR,)
4R (6.) and CRo,b)
bc
(9,b)
R
2,33 AEder
C2,),I,DY
tte Not
R=
3Not
ihua Co,c) cb,c)Rfa,b),
)ek (a, ’ eR
Cb.c) b)eR4 Ca,
A
Belatiba anaitiu
Bet
Dale
'ane No
Dale
R
TAanelu
R CL,2, (3,)} Transiliu
a, b
R:
R= AXA (Uniuat)
bfoanauu
A=fl2,34
X
Ri U), (2,2), Ci,3, (3,
R: fc), C2,3), (22, C3,2), (2,))
R= C2?), (2,)
R=fi2), c2,D, (,3, (3,D)
Al2,3 Dewkled pass tsanain
Rz ,1), (2,2), (3,5), 4,3), (2,3)Y x
R f ) , (2,2), (4,,(3,)y x
Ri 2),( ) 2,), (3,2, (a,2Dy x
Trani tiue
(22),"C,D} Transilie
/Pane N
Dale.
kquvalance Relae
helatiou
wela
tycuuitiuu
Shaw that Rlo.b)a 2diudu
l, 2,3 4, S,,6, , 8, 1} giuenby
equivalnee elatou
eruvalener Relaioin (R,s, T)
fo al a eA 2
Diuibu
(a,a) eR
oder (a, b) eR
ab= Diuieible bu 2 - 2mre
b,a) eR
traratie
i (a,6)ER (b, c) eR
det (a,b)eR
b-C 2D
Pagu Nu
Date
abtC 4+2p
(0,c)eR
Hince, t anditfue
Paoe ho
Dale
Yactica Qualow
+he
4trheitiu.
elatios a agorit,"yomté
RulatiouR
R-{l3), Ca, c),(,3), cA,112,(S9
1,D ¢ R eAauipli)
3) ¢ s
A CI,3) eR
ER Cb,c)
(9,c),9) ¢R
Nor traiu
C1,
)} (3,2), f!2), SoR:
ff.s), sos (a,1) C3,S,s),
2), Re
Ro
Bos RoR, SoR) (Ro
soR, Ros, find
(3,),(0,3)} (2,s),
Qic4,2),
2,2)y (3,),
RaCl22,
2,Rosef-y,4,),
} (9.j),
os. oupute
Ca,4)y (2,p), CL,4), f0,p), R=
P4AY B
,2,33 tzanhls
sy e,c) AXC
and Ca,Oe e
-Lowe
B,be Ros
ueee
RoS The
,e
Bx Bto MOW latipu the
AXRC
Bie, to uDmA tuóu ula th
esotA er
Relatiud CompaaloandcnNo A,B
)VI/
Ruh, SoR4
R fC)0,9, )
Ros fC1, 1), (2,), (,)3
Seki f C2), (2,),
Ro(soR): Ro fci,), (2,,
0ate
Patial
Au said to be an
Qidor Relalisn
uiymmlaie Traniile .
xiu,ie, (a,aeR,ae A
R
ntiymmahic ,iet a, beA and
Riu trailiue }e tob.c et and Ca, b)ER
and b,ocR Hen
Ca,)eK
y A l,2,3
X
Anti
RejloriasTrnetiu
Synbu
Ky} CD, (22), ( 33), C1,2), (2,D3
Rajaziua, Autisyumatac X
Ry,), (2,2), (3,9 (i,3),(2,3 Anty me
trliymnte-X
Page Nr
Date
A ja, b,c}
Ch, b), Ce,c),(a,D, C6, a)')
R: f(a,a),
Rejtaire k-- aRa
ntiey mmcie i- X
set 'A' uiapatinl adii.
POSET:A alled Pose
RelationR olinLdl on
Ez Afl,2,3}
(2,22, (o,3),C,22, (a,1), C), 3),)
R fi
ToraneiiL
