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 be the set of all finite sets. That is, elements of are finite sets. Define a relation Q on by AQB there is a bijection from A to B. This is an equivalence relation. Consider the quotient set . Define a relatoin R on 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] [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*]
[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.