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