Math Is Fun Forum

MogiYagi

Guest

Set theory - counterexamples!

Hi!

First off, thank you for the help I recieved yesterday, it greatly helped me.
Now I have another problem.

I'm supposed to prove if these statements are correct:

a) Bc = (A ∪ C) \ B

c) Ac ∪ Bc ∪ C
c = (A ∪ B ∪ C)c

What I did was I broke everything down into right- and left tables, and I saw disrepancy which proved that both the answers are not correct. This was not enough though. What I have to do is:

Counterexamples must contain elements , and a basic amount U, and it should be clear what the contradiction arises from and what you draw for conclusion.

How do I give an counterexample to prove that this is not correct? Please help!

Greetings!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Set theory - counterexamples!

hi MogiYagi

I'm assuming that Ac means the complement of A.

What I did was to draw a Venn diagram and shade the regions.

A u C = {d, e, f, g, h, i}

so

A u C | B = {g, h, i}

whereas

Bc = {g, h. i, k}

Clearly, these differ by the element k.

You can do a similar thing for the second one.

If you prefer you can make up sets like A = {those who play tennis} and put in some names.  Just make sure that you have something that corresponds to 'k'.

Hope that helps,

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

MogiYagi

Member

Registered: 2014-10-06

Posts: 2

Re: Set theory - counterexamples!

Thank you for the reply bob bundy, I really appriciate it!

Could you please look into my other thread regarding deduction and reduction and see if you could help me out a bit on that one too!

I've done alot of work on it already, but it seems my thinking was "off" somewhere in the process.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Set theory - counterexamples!

hi MogiYagi

I did look at the deduction and reduction thread, but I am unfamiliar with this method and notation.  I can prove / disprove a statement like this by means of a truth table, and maybe by simplifying the expressions  but the layout of your proof means nothing to me.  Sorry.  :-(

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob