
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 15th, 2017, 04:15 AM  #1 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 148 Thanks: 1  Property verification
Hello Please let me know if the below property is always true or does it need any additional conditions!!! Let X be a set. For $\displaystyle A \subset X $, let $ A^c = XA$. The correct statement for $\displaystyle A ,B \subset X $ is: A) $AB=B^c A^c$, always B) If $AB=B^c A^c$ then $\displaystyle A \subset B $ or $\displaystyle B \subset A $. C) If $AB=B^c A^c$ then $\displaystyle A \cap B = \emptyset $ D) If $AB=B^c A^c$ then $A=X $ or $B=X$ I think its always true because I checked the other 3 options. Please let me know if I'm wrong 
May 15th, 2017, 01:48 PM  #2 
Member Joined: Jan 2016 From: Athens, OH Posts: 44 Thanks: 26 
You're right. For any subsets S and T, $ST=S\cap T^c$. So $$B^cA^c=B^c\cap(A^c)^c=B^c\cap A=A\cap B^c=AB$$ 
May 15th, 2017, 05:53 PM  #3 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 148 Thanks: 1  

Tags 
property, verification 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
subspace verification  jubayer  Linear Algebra  0  November 27th, 2012 07:56 AM 
Probability HW verification  borogirl09  Probability and Statistics  3  October 10th, 2012 11:58 AM 
Verification: Prove if z is even then both x and y are even  restin84  Number Theory  6  April 6th, 2012 10:42 AM 
Verification: if 4(n3) then 8(n^2  1)  restin84  Algebra  2  March 27th, 2012 11:23 PM 
Need Verification  aqj_arnold2  Algebra  3  February 4th, 2009 09:26 PM 