Dr. Maths Replied.

Date: 03/18/2009 at 09:21:35
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.