Filling in the blanks proof, having some issues Set Theory Unions/Subsets

In summary, the conversation discusses a problem in a book where one must fill in missing spots in a proof regarding set subsets. The conversation also includes a link to the directions for the problem and a definition of the union of sets. The summary also mentions that the proof provided in the book may not match up with the directions given.
  • #1
mr_coffee
1,629
1
Hello everyone. Our book has a problem where we are to fill out the missing spots and its quite confusing, I'm not sure if i got this right or not.
Any help would be great!

Here is the question/directions:
The following is a proof that for all sets A and B, if A is a subset of B,
then A U B subset B. Fill in the blanks.

note: i didn't nkow how to write the subset symbol, so if you look at (a) u will see what is to be proved

http://suprfile.com/src/1/3onjybq/lastscan.jpg [Broken]
If you can't read it, here is what the book has:

Proof: Suppose A and B are any sets and A is a subset of B. We must show that (a). Let x be in (b). We must show that (c). By Definition of union, x in (d) (e) x in (f). In case x in (g), then since A is a subset of B, x in (h). In case x in B, then clearly x in B. So in either case, x in (i) as was to be shown.The defintion of union out of this book is the following, which didn't match up to will with th efill in the blanks (d), (e), and (f).

The union of sets x and Y, X U Y, is deifned as X U Y = {x | x in X or X in Y}

This means that any time you know an element x is in X U Y, you can concludde that x must be in X or x must be in Y. Conversely, any time you know that a particular x is in some set X or is in some set Y, you can conlucde that x is in X U Y. Thus, for any sets X and Y and any element x,

x in X U Y if, and only if, x in X or X in Y.Thanks.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
the proof looks good
 

1. What is a "filling in the blanks" proof in set theory?

A "filling in the blanks" proof in set theory is a method used to prove a statement about sets by filling in the missing elements or subsets. This involves starting with a general statement and then narrowing down the specific elements or subsets that satisfy the statement. It is a useful technique for proving complex statements about sets.

2. What are unions in set theory?

In set theory, a union is an operation that combines two or more sets and results in a new set that contains all the elements from the original sets. This can be represented by the symbol ∪ and is often used to find the total number of elements in multiple sets without counting any duplicates.

3. How do you determine if one set is a subset of another set?

A set is considered a subset of another set if all of its elements are also elements of the larger set. This can be determined by comparing the elements of the two sets and seeing if they match. If the smaller set has at least one element that is not in the larger set, then it is not a subset.

4. What are some common issues that may arise when working with set theory unions and subsets?

One common issue is determining the correct notation to use when representing sets and their operations. It is important to use the correct symbols and notation in order to accurately convey the relationships between sets. Another issue is understanding the properties and rules of set operations, which can sometimes be counterintuitive and may lead to mistakes in proofs or calculations.

5. How can filling in the blanks proofs help in understanding set theory?

Filling in the blanks proofs can help in understanding set theory by providing a concrete and systematic approach to proving statements about sets. By breaking down a complex statement into smaller, more manageable parts, it can make it easier to understand the relationships between sets and how they can be manipulated through operations like unions and subsets. Additionally, filling in the blanks proofs can help to identify any errors or inconsistencies in a statement, leading to a deeper understanding of set theory concepts.

Similar threads

  • Calculus and Beyond Homework Help
Replies
1
Views
457
  • Calculus and Beyond Homework Help
Replies
2
Views
829
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
11
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
899
Back
Top