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- New Jersey
- Rutgers University - New Brunswick/Piscataway
- Mathematics
- Mathematics 300
- Rodney
- MATH 300 midterm

Crystina M.

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}

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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}

1. if Xe*A*, thenX ="empty set" 2. if Xe

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

linear order on A

if for any 2 elements x&y of A either xRy or yRx

function from A->B

1. the dom of f is A

2. if (x,y)ef & (y,z)ef, then y=z

2. if (x,y)ef & (y,z)ef, then y=z

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Restriction of f to D

f/_{D} ={(x,y): y = f(x) and xeD}

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

iff Rng(f)=B

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

when...f(x) = f(y), then x=y

1-1 correspondence

iff f is 1-1 and onto B

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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