How to Prove it book help with ch 1.4 operation on sets problem (symmetric diff)

  • Thread starter Thread starter Gerlan_au
  • Start date Start date
  • Tags Tags
    Book Sets
Click For Summary

Homework Help Overview

The discussion revolves around verifying the identity involving symmetric differences and intersections of sets, specifically the expression (A ∩ B) Δ C = (A Δ C) Δ (A \ B). The subject area is set theory, focusing on operations involving sets and their visual representations through Venn diagrams.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss their attempts at using Venn diagrams to represent the left and right sides of the identity. There are questions about the correctness of these diagrams and the interpretation of the symmetric difference. Some participants express confusion regarding the intersections and unions involved.

Discussion Status

Several participants have provided feedback on each other's diagrams, suggesting corrections and improvements. There is an ongoing exploration of the visual representation of the sets, with some participants questioning their understanding and seeking clarification on specific aspects of the problem.

Contextual Notes

Participants mention that the textbook does not provide solved examples for similar problems, contributing to their uncertainty. There is also a sense of fatigue expressed by one participant after extensive work on the problem.

Gerlan_au
Messages
5
Reaction score
0

Homework Statement



Use any method you wish to verify the following identity:

(A \cap B) Δ C = ( A Δ C) Δ (A \ B)

Homework Equations



A Δ B = (A \ B) \cup (B \ A) = (A \cup B) \ (A \cap B)

The Attempt at a Solution



http://img17.imageshack.us/img17/48/14question14b.jpg


I think my attempt at the left hand side Venn diagram ((A \cap B) Δ C) is incorrect as the right hand side states that x \notin B, so I am left very confused :(
 
Last edited by a moderator:
Physics news on Phys.org
Gerlan_au said:

Homework Statement



Use any method you wish to verify the following identity:

(A \cap B) Δ C = ( A Δ C) Δ (A \ B)

Homework Equations



Definition of A Δ B :

A Δ B = (A \ B) \cup (B \ A) = (A \cup B) \ (A \cap B)

The Attempt at a Solution



[ IMG]http://i.imgur.com/cmOJv.jpg[/PLAIN]

I think my attempt at the left hand side Venn diagram ((A \cap B) Δ C) is incorrect as the right hand side states that x \notin B, so I am left very confused :(
You should really reduce the size of that image you posted.

I take it that the Δ symbol stands for the symmetric difference of two sets.


The figure you show seems nonsensical .
 
Thank you for replying, resized the image, and yes the Δ stands for symmetric difference, I also think that my original attempt at the solutions is incorrect, could you possibly point me to the right direction?

The book itself did not have any solved solutions for similar problems so I cannot confirm if my solution is correct or not and it is bugging the hell out of me >< (obviously the solution is not correct :P)
 
Your very first diagram for (A ∩ B) Δ C is wrong. Try drawing (A ∩ B) first. The second one for (A Δ C) looks ok. The third one for (A \ B) is also wrong. If you are going to put this all together with Venn diagrams you need to correct some of the parts.
 
Thanks for the reply sir! :)

I have tried to correct my diagram and came up with this, is that in the right direction? (I think for (A ∩ B) Δ C I should remove the intersection between B and C )

http://img152.imageshack.us/img152/4692/14question14battempt2.jpg
 
Last edited by a moderator:
Gerlan_au said:
Thanks for the reply sir! :)

I have tried to correct my diagram and came up with this, is that in the right direction? (I think for (A ∩ B) Δ C I should remove the intersection between B and C )

http://img152.imageshack.us/img152/4692/14question14battempt2.jpg

The symmetric difference should be everything that is in (A ∩ B) or C but not in A ∩ B ∩ C. Right? You've still got the same diagram as in the original post. I think you need to remove some stuff and add some stuff.
 
Last edited by a moderator:
Hmmm, would that be correct then?

http://img89.imageshack.us/img89/9255/14question14battempt3.jpg

Thank you very much for taking the time to help me though! At the moment I've been working on the problems from that chapter for the better part of 5 hours and I do not think I can think straight anymore lol, so if my above correction is wrong I might take a break and return to that question tomorrow as my brain is already fried :(
 
Last edited by a moderator:
Gerlan_au said:
Hmmm, would that be correct then?

http://img89.imageshack.us/img89/9255/14question14battempt3.jpg

Thank you very much for taking the time to help me though! At the moment I've been working on the problems from that chapter for the better part of 5 hours and I do not think I can think straight anymore lol, so if my above correction is wrong I might take a break and return to that question tomorrow as my brain is already fried :(

That's right! Take a break or try to fix the third diagram. That's an easy one. Your choice.
 
Last edited by a moderator:
Alright so I tried to take a break from that problem but it is still in the back of my head and I think i may have found a solution!

http://img7.imageshack.us/img7/9255/14question14battempt3.jpg

Is that right?! Am I close?! or am I just going insane and have not noticed it hah!
 
Last edited by a moderator:
  • #10
Gerlan_au said:
Alright so I tried to take a break from that problem but it is still in the back of my head and I think i may have found a solution!

http://img7.imageshack.us/img7/9255/14question14battempt3.jpg

Is that right?! Am I close?! or am I just going insane and have not noticed it hah!

I'm not sure whether it's right or not. What's it supposed to be?
 
Last edited by a moderator:
  • #11
Gerlan_au said:
Alright so I tried to take a break from that problem but it is still in the back of my head and I think i may have found a solution!

http://img7.imageshack.us/img7/9255/14question14battempt3.jpg

Is that right?! Am I close?! or am I just going insane and have not noticed it hah!
I'm pretty sure that the question Dick was asking was, What is this the Venn of ?

Can't say it's right or that it's wrong without knowing what it refers to.

I'm sure Dick can write an expression which corresponds to this Venn diagram. On a good day, so can I.
 
Last edited by a moderator:

Similar threads

Replies
16
Views
4K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
2
Views
2K
Replies
10
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 10 ·
Replies
10
Views
12K