
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 14th, 2018, 09:22 AM  #1 
Newbie Joined: Oct 2018 From: Turkey Posts: 23 Thanks: 0  Number of elements in set
A N B is not empty set A U B has 17 elements Number of subsets of A N B = n (A  B) Theb what is the minimum number of elements of B? Answer is 9 but i can not get there I drew Venn diagram and said a+b+c = 17 (these are my cariables), 2^b = a and then 2^b + b +c = 17 But then couldn't solve. (N is for intersection set, and n is for number of elements ) 
November 14th, 2018, 11:52 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,324 Thanks: 1233 
$A \cap B \neq \emptyset$ $A \cup B  = 17 = A + B  A \cap B$ $2^{A \cap B} = AB = A  A \cap B$ $A  A \cap B = 17  B$ $2^{A \cap B} = 17  B$ $B = 17  2^{A \cap B}$ $A \cap B=4 \Rightarrow B=1$ But this is impossible as $A \cap B \leq B$ $A \cap B = 3 \Rightarrow B=9$ This is perfectly valid. Further reducing $A\cap B$ just increases $B$ and thus $B=9$ is the minimum value. 
November 15th, 2018, 01:34 AM  #3  
Newbie Joined: Oct 2018 From: Turkey Posts: 23 Thanks: 0  Quote:
 
November 15th, 2018, 04:15 AM  #5  
Newbie Joined: Oct 2018 From: Turkey Posts: 23 Thanks: 0  Quote: \alpha well i couldnt do it i mean how do you write those symbols in here...  
November 15th, 2018, 04:47 AM  #6 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,043 Thanks: 817 Math Focus: Wibbly wobbly timeywimey stuff.  

Tags 
elements, number, set 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Number of elements in intersection set  ketanco  Probability and Statistics  5  December 4th, 2018 11:50 AM 
How do I find the least number of elements in a series of sets?  Chemist116  Elementary Math  2  February 27th, 2018 06:23 AM 
number of elements  jroff419  Probability and Statistics  2  May 4th, 2017 10:14 PM 
Maximum number of elements in set.  fidanym  Topology  4  October 28th, 2014 03:15 AM 
determining the number of elements in a group  blondie16  Linear Algebra  1  April 28th, 2011 09:38 AM 