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Cartesian product

A X B:

A X B = {(a,b): a eA and beB}

Dom(R)=

Rng(R)=

{xeA: there exists yeB such that xRy}

{yeB:there exists xeA such that xRy}

Identity relation on A

I_{A }= {(x,x):xeA}

inverse of R

R^{-1} ={(y,x):x,y e R}

the composite of R and S

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}

Let R be a partial order for A and B

( upper/lower bounds)

least upper bound

greatest lower bound

linear order on A

function from A->B

Restriction of f to D

A function f:A->B is onto B (surjection)

A function f:A->B is 1-1 (injection)

1-1 correspondence

image set of X

inverse image of Y

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