Subsets Definition and 209 Threads

Suppose f:A--->B and S and T are subsets of A. Prove or give a counter example. (a) if S\subseteqT, then f(S)\subseteqf(T) (b) if f(S)\subseteqf(T), then S\subseteqT I know for a fact that (a) is true. The reason I say this is because if S\subseteqT ... then for example: Let S be the...

I have been reviewing my set theory and topology and recently came across an assertion I was not familiar with, and frankly have trouble grasping. In words, let I be a set (which is to serve as the set of indices), then for each \alpha \in I let A_\alpha be a subset of some set S. Now...

I'm just an interested laymn, and I'm trying to improve my knowledge in some areas where I'm weak. To this end, I found that Shilov's Elementary Real and Complex Analysis was highly recommended, and the Dover edition was available for only ten bucks, so how could I go wrong? But it didn't take...

Hi, I am having trouble with these proofs; I don't know if I am doing these right. I'd appreciate some help. Thank you. If X---> y is a map, then let B1, B2, B \subseteq X. i. f(B1 U B2) = f(B1) U f(B2) To prove this I have: f(B1 U B2)=f(B1) U f(B2) Since B1 U B2 \subseteq B1, we...

Having some difficult with general concepts of metric spaces: 1) What is the difference between a subset and a subspace. let's say we have metric space X. and A is a set in that space. Is A necessarily a metric space itself? 2) Why is the metric of X ( d(x,y) for x,y belonging to X )...

1. If a school offers 3200 separate courses and a survey of these courses determines that the class size is 50 with a standard deviation of 2, what would one expect for the average and standard deviation of a subset of 50 of these classes selected randomly? 2. In a survey to estimate the...

By definition, an infinite set is a set whose subset is proportional to the set which contains it. The sequence of numbers whether it be expressed as (n+1) or not, is infinite. Then (I am veturing into grounds I know little of here...) I am guessing it is safe to say that the numbers (n+1< or...

Show that the subsets of the plane are open: 1.) A= {(x,y)|-1<x<1,-1<y<1} 2.) C= {(x,y)|2<x2 + y 2<4} I have no clue on how to start with this problem. I have another question. What does this notation imply. f(x,y)=some function.

Hello, I am supposed to show that the number of proper subsets of S = {a1, a2, ... an} is 2^n - 1. I know that the number of subsets of S is 2^n. And I know also know that the number of proper subsets of S is 2^n - 1 since S is not a proper subset of itself. But how do I show that? I...