My Math Forum > Math Laws of Algebra, Set Theory problem

 Math General Math Forum - For general math related discussion and news

May 26th, 2015, 05:32 AM   #1
Newbie

Joined: May 2015
From: tiong barhu

Posts: 3
Thanks: 0

Laws of Algebra, Set Theory problem

Anyone know how to do this question? Im stuck at (A n B) n (A n Bc) after using demorgan's law. TIA-
Attached Images
 20150526_210016.jpg (92.4 KB, 1 views)

 May 26th, 2015, 09:13 AM #2 Senior Member   Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 Take an example, such as $A=\{1,2,3\}$, $B=\{3,4,5\}$ and the universal set $U=\{1,\dots,10\}$. Compute $A\cap B\cap A\cap B^c$. This may give you a hint for a general proof. Thanks from weijiang
May 26th, 2015, 09:41 AM   #3
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Hello, weijiang!

Quote:
 Anyone know how to do this question? $\;\;\;(A\,\cap\,B)\,\cap\,(A^c\,\cup\,B)^c \:=\:\emptyset$

$\begin{array}{cccccccc}
1. & (A\,\cap\,B)\,\cap\,(A^c\,\cup\,B)^c &\;\;& 1. & \text{Given} \\ \\
2. & (A\,\cap\,B)\,\cap\,(A\,\cap\,B^c) && 2. & \text{DeMorgan} \\ \\
3. & A\,\cap\,(B\,\cap\,A)\,\cap\,B^c && 3. & \text{Associative} \\ \\
4. & A\,\cap\,(A\,\cap\,B)\,\cap\,B^c && 4. & \text{Commutative} \\ \\
5. & (A\,\cap\,A)\,\cap\,(B\,\cap\,B^c) && 5. & \text{Associative} \\ \\
6. & A \,\cap\,(B\,\cap\,B^c) && 6. & S\,\cap\,S \:=\:S \\ \\
7. & A\,\cap\,\emptyset && 7. & S\,\cap\,S^c \:=\:\emptyset \\ \\
8. & \emptyset && 8. & S\,\cap\,\emptyset \:=\:\emptyset
\end{array}$

May 26th, 2015, 04:57 PM   #4
Newbie

Joined: May 2015
From: tiong barhu

Posts: 3
Thanks: 0

Quote:
 Originally Posted by soroban Hello, weijiang! $\begin{array}{cccccccc} 1. & (A\,\cap\,B)\,\cap\,(A^c\,\cup\,B)^c &\;\;& 1. & \text{Given} \\ \\ 2. & (A\,\cap\,B)\,\cap\,(A\,\cap\,B^c) && 2. & \text{DeMorgan} \\ \\ 3. & A\,\cap\,(B\,\cap\,A)\,\cap\,B^c && 3. & \text{Associative} \\ \\ 4. & A\,\cap\,(A\,\cap\,B)\,\cap\,B^c && 4. & \text{Commutative} \\ \\ 5. & (A\,\cap\,A)\,\cap\,(B\,\cap\,B^c) && 5. & \text{Associative} \\ \\ 6. & A \,\cap\,(B\,\cap\,B^c) && 6. & S\,\cap\,S \:=\:S \\ \\ 7. & A\,\cap\,\emptyset && 7. & S\,\cap\,S^c \:=\:\emptyset \\ \\ 8. & \emptyset && 8. & S\,\cap\,\emptyset \:=\:\emptyset \end{array}$
thanks! By the way how you use associative on
(A n B) n (A n Bc) since the rule for associative is
(A n B) n C to A n (B n C) which has only a bracket? I dont understand this part

Last edited by weijiang; May 26th, 2015 at 05:01 PM.

May 26th, 2015, 04:59 PM   #5
Newbie

Joined: May 2015
From: tiong barhu

Posts: 3
Thanks: 0

Quote:
 Originally Posted by Evgeny.Makarov Take an example, such as $A=\{1,2,3\}$, $B=\{3,4,5\}$ and the universal set $U=\{1,\dots,10\}$. Compute $A\cap B\cap A\cap B^c$. This may give you a hint for a general proof.
Thank you

 Tags algebra, laws, problem, set, theory

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post cecilia777 Computer Science 0 June 8th, 2013 05:23 AM Turk Number Theory 1 September 20th, 2012 05:48 PM sallyyy Algebra 2 December 31st, 2010 09:35 AM hky Applied Math 0 December 31st, 1969 04:00 PM cecilia777 Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top