# subset

1. ### An "optional" proof

Let A, B⊆ U. Show that A ⊆ A - (B-A). Based on logic alone, I sort of figured out that even if I find (B - A), it would not matter because then I would be left with A - B, correct? However, I could be completely off in that notion.
2. ### Linear Algebra, meaning of R^m

The problem states: "Suppose that {v1,v2,v3} is a linearly independent subset of Rm." What does Rm in this case mean?
3. ### Help understanding this proof: E is a subset of f^(-1)(f(E))

\text{Let } f: X\rightarrow Y, \text{ where } X \text{ and } Y \text{ are sets.} \text{Prove that }E \subseteq f^{-1}(f(E)) \text{ } \forall E \subseteq X. PROOF: \text{Let } x \in E. \text{Then, }y = f(x) \in f(E), \text{ so } x \in f^{-1}(f(E)). \text{ Hence } E \subseteq f^{-1}(f(E)) How...
4. ### Need help verifying supremum and infimum of the subset.

For A = {0,1,2,3,4,5,7,8,9} , let B = {{2,3,4},{0,3,4,5,9},{0,2,3,8}} B is a subset of P(A). Using the partial order ⊆ for P(A) find inf(B) and sup(B). The first thing one must know in order to solve is to know what the spremum and infinmum is. The supremum is the upperbound other wise know as...
5. ### Proof of a coset being a subset

​Hello all, after wrestling around with this proof for the better part of an hour, I think I got it. If I am wrong, PLEASE do not give the answer! Just a simple hint would be most appreciated. The question is to suppose that H and K are subsets of G, and there are elements a,b in G such that...
6. ### Denumerability of a subset of a denumerable subset

The following is an excerpt from Serge Lang's "Real and Functional Analysis" In the proof, the author defines \left \{k...k_n \right \} as a subset of D. How does he know that D is big enough to contain a set of elements that can be indexed to n? I assume that, by n, the textbook means an...
7. ### Prove that each subset of a countable set is countable

I want to prove: Each subset of a countable set is countable. Here are the definitions available to me: Def: A set A is finite provided A is empty or there is a positive integer N for which there is a 1:1 correspondence between A and the integers 1 through N. A set which is not finite...
8. ### Help with a Subset Expression

Hi, I was hoping somebody could chime in on this problem and confirm my answer. It asks, "Which of the diagrams below, left or right, shows a shaded area that represents the expression: [A U B]^c ∩ C (The ^c is the complement) First image has only C shaded and the second has C, A ∩ C, and B...