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Cartesian product
A X B:
Dom(R)=
Rng(R)=
{xeA: there exists yeB such that xRy}
{yeB:there exists xeA such that xRy}
I_{A }= {(x,x):xeA}
S * R ={(a,c) :there exists beB such that (a,b)eR & (b,c)eS
X Mod R
A Mod R
X/R = {yeA: xRy}
A/R: {x/R: xeA}
1. if XeA, thenX ="empty set" 2. if XeA and YeA , then X=Y or X ^Y="e.s" 3 . U_{xeA }X= A
Let R be a partial order for A and B
( upper/lower bounds)
aeA is an upper bound for B if for every beB, bRa
aeA is a lower bound for B if for every beB, aRb
least upper bound
greatest lower bound
if a is an upper bound for B & aRx for every upper bound x for B.
if a is a lower bound for B & for every lower bound x for B, xRa
when...f(x) = f(y), then x=y
image set of X
inverse image of Y
f(X) = {yeB: y =f(x) for some xeX
f^{-1}(Y) = {xeA: f(x)eY}
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