Originally Posted by
IHateProofs So after looking through months of old notes I think I finally found how to do (a). This is what I have.
Proof: We will prove this by showing that R possesses the reflexive, symmetric, and transitive properties. First we will prove that R is reflexive. Observe X ∩ B = X ∩ B. Therefore XRX and R is reflexive. Next assume XRY. Then X ∩ B = Y ∩ B. Hence Y ∩ B = X ∩ B. Therefore YRX and R is symmetric. Finally, assume XRY and YRZ. Then X ∩ B = Y ∩ B, and Y ∩ B = Z ∩ B. Hence X ∩ B = Z ∩ B. Therefore XRZ, and so R is transitive. Since R possesses the reflexive, symmetric, and transitive properties, it follows that R is an equivalence relation.
But I still can't figure out (b). I can't find anything in my old assignments about the equivalence class of a subset. If I had to guess, I'd say the answer is the super set of X ∩ B = (1,3). So [X]= {(1,3), X, (1,3,4), B, (1,2,3,4), (1,2,3,5), (1,3,4,5), A}. Is that right?