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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: 2,203 Thanks: 1157 
$A \cap B \neq \emptyset$ $A \cup B  = 17 = A + B  A \cap B$ $2^{A \cap B} = AB = A  A \cap B$ $A  A \cap B = 17  B$ $2^{A \cap B} = 17  B$ $B = 17  2^{A \cap B}$ $A \cap B=4 \Rightarrow B=1$ 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: 1,922 Thanks: 775 Math Focus: Wibbly wobbly timeywimey stuff.  

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