# finite set and equivalence reltion

• Mar 31st 2009, 02:42 PM
scottie.mcdonald
finite set and equivalence reltion
This question is confusing me, and I do not know what information is needed to solve the problem. Here is the question:

let $\displaystyle \beta$ be the set of all finite sets. That is, elements of $\displaystyle \beta$ are finite sets. Define a relation Q on $\displaystyle \beta$ by AQB $\displaystyle \Leftrightarrow$ there is a bijection from A to B. This is an equivalence relation. Consider the quotient set $\displaystyle \frac{\beta}{Q}$. Define a relatoin R on $\displaystyle \frac{\beta}{Q}$ by [A]R[B] if there is an injection from A to B

a). show that R is well defined: If [A]=[A*] and [B]=[B*] then [A]R[b] $\displaystyle \Leftrightarrow$ [A*]R[B*]
b). show that R is reflexive.
c). show that R is transitive.
d). show that R is antisymmetric

what i have so far is follows:

injective: [A]=[A*] and [B]=[B*]
$\displaystyle \Rightarrow$ [A]R[A*] and [B]R[B*] then my mind goes completely blank. i need to show injective and surjective (onto and one-one), but the orginal information i can't understand.

Thank you,

Scott
• Mar 31st 2009, 02:44 PM
scottie.mcdonald
all of the letters A and B are supposed to be capitalized. I've tried editting them, but it wouldn't convert over. sorry if it's confusing.
• Mar 31st 2009, 03:00 PM
Plato