From: Doctor Fenton

To: jiachiun@gmail.com (Xeleon)

Subject: Re: About Sets. Shade the region of B \ A'

Hi,

Thanks for writing to Dr. Math. You might ask your instructor for

his definition of the relative complement B\C of C in B, but the

definition I know is that it is the set of all elements of B which

do not belong to C. (See

http://en.wikipedia.org/wiki/Relative_complement#Relative_complement ,

so Wikipeida agrees with what I learned.)

That means that for any set C, B\C is a subset of B, so it cannot

include any elements of B', and diagram (ii) cannot be the answer.

I agree with you.

The Wikipedia article also notes the set relationn

B\C = B ^ C' (where ^ denotes intersection).

Using that relation,

B\A' = B^(A')'

= B^A

the intersection of A and B, which is exactly what diagram (i) shows.

I agree with you.

If you have any questions, please write back and I

will try to explain further.

- Doctor Fenton, The Math Forum

<http://mathforum.org/dr.math/>

The Math Forum @ Drexel is a research and educational enterprise

of the Drexel School of Education: <http://www.drexel.edu/soe/>

Date: 03/18/2009 at 06:44:24

From: jiachiun@gmail.com (Xeleon)

To: dr.math@mathforum.org

Subject: About Sets. Shade the region of B \ A'

[Question]

My question is simple, but I'm confused. Which of the following

represents the region of B\A' ?

(i) (ii)

+---------------------+ +---------------------+

| | |:::::::::::::::::::::|

| +-----+ | |::::+-----+::::::::::|

| / \ | |:::/ \:::::::::|

| + + | |::+ +::::::::|

| | A | | |::| A |::::::::|

| + +--+--+ | |::+ +--+--+:::::|

| \ /::/ \ | |:::\ /::/ \::::|

| +--+--+ + | |::::+--+--+ +:::|

| | B | | |:::::::| B |:::|

| + + | |:::::::+ +:::|

| \ / | |::::::::\ /::::|

| +-----+ | |:::::::::+-----+:::::|

| | |:::::::::::::::::::::|

+---------------------+ +---------------------+

[Difficulty]

I've learned sets in my high school long ago.

My answer is (i).

But now in my college, my lecturer said (i) is wrong, and the answer

is (ii).

I'm confused.

[Thoughts]

He told me B\A' is that since B is "smaller" than A', and B cannot

completely minus A', we have to remove the common parts of B and A'

and then add up the remaining (the "negative" part), which then came

out with the answer (ii).

I then told him he might have mistaken this with the Symmetric

Difference. (i.e B Δ A' ) and added that if it's Symmetric

Difference, then the answer will be (ii).

But he paid no attention to my "Symmetric Difference". He continued on

his theory. He said my answer (i) will be correct if the question did

not mention the universal set (that means without the 'square'). But

if there is universal set, then (ii) will be the answer.

I am more and more confused.

I believe I am right and he is wrong, but I find no way to convince

him. And I don't know which answer to choose if this comes out in the

exam.

Please tell me what can I do, or correct me if I'm wrong.

Thanks a lot. :)

[Refer to my previous post "I think my Maths is getting worse"]

[Updated as of 19 March 2009]

Those who agreed with answer (i):

1. Jia Chek (my bro)

2. Woei Chean (a Maths genius from my high school)

3. Pei Yun (a Maths genius too,according to my observation)

4. Justice (bear bear XD)

5. Bubbles (not the one from powerpuff girl)

6. Tzi Jia (a happy-go-lucky girl, cheerful!)

7. Dr. Maths (someone from http://mathforum.org/dr.math/)

Those who agreed with answer (ii):

1. Mr. K*****N (my current Maths lecturer)

2. Fleo (a great friend of mine)

so it's 7:2 now..! :D

hmph..!

(but why am I doing these.. arghh...)

Just ignore me if you are offended or leave a comment if you concern.

Another thanks in advance. :]

p.s I'm now acting like a lil kid who has just got scolded by a teacher but find no way to fight back. And so getting witnesses/supports and gathering information trying to point that the teacher is wrong and he himself is right.

How childish it is.

But that's exactly what I'm doing now.

and that's me.

Yes, I'm naive.

But I just want to know the right answer.

You will get upset when your teacher insists that you are wearing your shirt inside out when you think you are actually not, won't you?

And you try to convince the teacher that you are wearing it right but your teacher still insists that you are wrong and threw you a lot of theories that you think doesn't make sense at all.

And you have been wearing like this for the past few years, people all over your hometown have been wearing exactly the same and nobody ever said it is wrong but now your teacher said you are wrong.

How do you feel?

Will you ignore them and stick with your own principle, taking the risk that your marks might be deducted in the exam for wearing "untidy" clothes into the examination hall and laughed by everyone for being stubborn?

or will you change your principle and follow whatever the teacher said as long as it pleases your teacher, but taking the risk that your marks might also be deducted as you think that if the examiner is another teacher, he might have a different view and say you're wrong again?

This post is written in a rush. I'm hungry. And the class starts soon. jolly.

## 4 comments:

Did you draw that thing?

Wah.

Anyway, I feel you la. I've experienced that before, only in a different sense.

well....im really returned all i learned back to teacher...

@panda: yeap, nvm, feel much better now, I found a number of proofs already, (after scanning through the books all over the library) lol.. but guess I'm not going to argue with him anymore. :]

@fleo : lol, it's normal, don't worry :) It's just the matter of time, I will too eventually return all of them to the teacher when no more revision is done ><"

Everything fades with time.

walaoA.. i hav nth to say ><

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