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November 14th, 2018, 09:05 AM  #1 
Newbie Joined: Oct 2018 From: Turkey Posts: 23 Thanks: 0  Number of elements in intersection set
A and B are two sets. A N B is not empty set and n ((AB)) U (BA)) = 26 and n (A) =20 . What is the minimum number of elements B must have ? N denotes intersection, n denotes number of elements Answer is 8 but why? I said A has 19, intersection has 1, and BA = 6 , So this makes B having 6+1 = 7 but why is answer 8 ? 
November 15th, 2018, 12:00 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,316 Thanks: 1230 
$(AB) \cup (BA) = A + B  2A \cap B = 26$ $A = 20$ $(AB) \cup (BA) = 20 + B  2A \cap B = 26$ $B = 6 + 2A \cap B$ $A \cap B \geq 1$ $B \geq 6 + 2 = 8$ 
November 15th, 2018, 01:41 AM  #3 
Newbie Joined: Oct 2018 From: Turkey Posts: 23 Thanks: 0  thanks and why do we subtract twice of intersection in the formula? is this a formula to memorize?

November 15th, 2018, 02:17 AM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,316 Thanks: 1230  
December 4th, 2018, 10:32 AM  #5 
Newbie Joined: Dec 2018 From: United Kingdom Posts: 2 Thanks: 0 
Does anyone know where I can answer questions like these? An online calculator or some sort?  Let A={1,2,3,4},B={3,5,7},C={2,3,4,5}A={1,2,3,4},B={3, 5,7},C={2,3,4,5} and D={6,7,8}  In the following, you may assume that N={1,2,3,4,....} and Z={...,−3,−2,−1,0,1,2,3,...} Which of the following apply?  And what can I use to find out how following statements are valid EG: {1,3,5,7,9,11,....}∪{2,4,6,8,10,....}=N 
December 4th, 2018, 11:50 AM  #6  
Senior Member Joined: Sep 2015 From: USA Posts: 2,316 Thanks: 1230  Quote:
Mathematica certainly can  

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