I have a question about members/subsets.
Let A be a nonempty set and let B be a subset of the power set $\mathcal{P} ({A})$ of A. Define a relation R from A to B by xRY if x ∈ Y. Give an example of two sets A and B that illustrate this. What is R for these two sets?
Say we take the set A = {1, 2, 3}. Let B be the subset of its powerset, say B = { {1}, {2}, {1,2} }. Then it seems to me that any element of A, say 1, is not an element of B. For example the element 1 is not a member of B, only the element {1} is. I'm obviously misunderstanding something though, so any help will be much appreciated.