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

1. Dec 16, 2012

### Gerlan_au

1. The problem statement, all variables and given/known data

Use any method you wish to verify the following identity:

(A $\cap$ B) Δ C = ( A Δ C) Δ (A \ B)

2. Relevant equations

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

3. The attempt at a solution

http://img17.imageshack.us/img17/48/14question14b.jpg [Broken]

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: May 6, 2017
2. Dec 16, 2012

### SammyS

Staff Emeritus
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 .

3. Dec 16, 2012

### Gerlan_au

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)

4. Dec 16, 2012

### Dick

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.

5. Dec 16, 2012

### Gerlan_au

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 [Broken]

Last edited by a moderator: May 6, 2017
6. Dec 16, 2012

### Dick

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: May 6, 2017
7. Dec 16, 2012

### Gerlan_au

Hmmm, would that be correct then?

http://img89.imageshack.us/img89/9255/14question14battempt3.jpg [Broken]

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: May 6, 2017
8. Dec 16, 2012

### Dick

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: May 6, 2017
9. Dec 19, 2012

### Gerlan_au

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 [Broken]

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

Last edited by a moderator: May 6, 2017
10. Dec 19, 2012

### Dick

I'm not sure whether it's right or not. What's it supposed to be?

Last edited by a moderator: May 6, 2017
11. Dec 19, 2012

### SammyS

Staff Emeritus
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: May 6, 2017