Set theory - expression describing subset

AI Thread Summary
To show that set E is a subset of set L using only complement, union, and the empty set, one can express it as complement(complement(E) union L) = Ø. This indicates that there are no elements outside of L that are also in E. A Venn Diagram can be a helpful tool for visualizing the relationship between the two sets. The discussion emphasizes the importance of understanding set operations in proving subset relationships. Clarity in these operations is crucial for solving such problems effectively.
tsrgb
Messages
3
Reaction score
0

Homework Statement


I have two sets E and L.
I have to show that E is a subset of L, using only complement, union and the empty set.
I.e. all members of E also have to be members or L, but L may contain members not included in E.

Homework Equations


The Attempt at a Solution


Am I right in describing it thus:
complement(complement(E) union L) = Ø

Any help is appreciated.tsrgb
 
Physics news on Phys.org
Its quite easy to work out or check your answers if you draw up a Venn Diagram =]
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Proof of Partition Property for Subset A in Universal Set U
Replies
1
Views
1K
I Construction of sigma-algebras: a counterexample
Replies
5
Views
2K
Proof about two disjoint non-empty sets ## S ## and ## T ##
Replies
11
Views
2K
I Help with basic transfinite induction proof
Replies
2
Views
2K
Prove relation between the group of integers and a subgroup
Replies
6
Views
1K
I On translation and dilation invariant Lebesgue measure: Folland's text
Replies
2
Views
2K
Defining Set Configurations with Properties and Functions
Replies
8
Views
2K
Understanding Subset Relations in Set Theory
Replies
1
Views
2K
Are the following statements true? (1) a∈{{a},{a,b}} and (2) b∈{{a},{a,b}} true?
Replies
8
Views
1K
Finding Complement of a set with respect to space U
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top