What does this mean,(A Δ B)^c?

  • Thread starter Thread starter matrix_204
  • Start date Start date
Click For Summary

Homework Help Overview

The discussion revolves around understanding the expression (A Δ B)^c, which refers to the complement of the symmetric difference between two sets A and B. Participants are exploring the definitions and implications of this notation in set theory.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the meaning of (A Δ B)^c and how to determine its value. There is a focus on understanding the complement of the symmetric difference, with some questioning how to express this complement in terms of the original sets.

Discussion Status

The discussion is ongoing, with participants providing insights into the nature of the complement and its relationship to the symmetric difference. Some have offered definitions and examples, while others express confusion about the specific expression and seek further clarification.

Contextual Notes

There is mention of a textbook not providing the complement's expression, which contributes to the participants' uncertainty and difficulty in progressing with related problems.

matrix_204
Messages
99
Reaction score
0
What does this mean,

(A Δ B)^c? And what does it equal to?

I know that (A Δ B)= (A-B) U (B-A).
 
Physics news on Phys.org
matrix_204 said:
What does this mean,

(A Δ B)^c? And what does it equal to?

I know that (A Δ B)= (A-B) U (B-A).

Might mean the complement of (A Δ B)
 
Yes, I know, but how do I find the complement. Thats where I'm stuck. What is the complement equal to?
 
matrix_204 said:
Yes, I know, but how do I find the complement. Thats where I'm stuck. What is the complement equal to?

I don't really understand what you are asking, the complement is going to be all members of the universe that are not in the given set so from what you have told me it would be the set of all x such that x is not a member of the symmetric difference between A and B.
 
So for example, all x such that x is not in (A Δ B)= (A-B) U (B-A)!
What I was asking is what's (A Δ B)^c= ??
Because in the textbook it's not given and I got stuck for one of the problems before I could proceed.
 
Note that your triangle thingy set does not contain points common to A and B, nor does it contain points in the complement of the union of A and B.

Does that help?
 

Similar threads

Formal Def of Limit: Why is |x-c| < δ and not |x-c| <= δ
  • · Replies 6 ·
Replies
6
Views
2K
Frequency Response Problem for given system
  • · Replies 1 ·
Replies
1
Views
2K
Prove that Lim x->c f(x)g(x)=0 if Lim x->c f(x)=0 and |g(x)|<K
  • · Replies 2 ·
Replies
2
Views
2K
Finding Limits Using the Epsilon-Delta Method
  • · Replies 8 ·
Replies
8
Views
2K
Vector Cross Product With Its Curl
  • · Replies 2 ·
Replies
2
Views
3K
How to calculate for Probability -- Summarized
  • · Replies 11 ·
Replies
11
Views
2K
High School When are two vectors collinear and coplanar?
  • · Replies 10 ·
Replies
10
Views
3K
What is the Inverse Laplace Transform of e^(-sx^2/2)?
  • · Replies 10 ·
Replies
10
Views
3K
Function Continuity Proof in Real Analysis
  • · Replies 8 ·
Replies
8
Views
2K
What Are Local Minimum and Maximum Points in Continuous Functions?
  • · Replies 30 ·
2
Replies
30
Views
3K