My Math Forum Number of elements in intersection set

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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 ((A-B)) U (B-A)) = 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 B-A = 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 $|(A-B) \cup (B-A)| = |A| + |B| - 2|A \cap B| = 26$ $|A| = 20$ $|(A-B) \cup (B-A)| = 20 + |B| - 2|A \cap B| = 26$ $|B| = 6 + 2|A \cap B|$ $|A \cap B| \geq 1$ $|B| \geq 6 + 2 = 8$ Thanks from ketanco
November 15th, 2018, 01:41 AM   #3
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Quote:
 Originally Posted by romsek $|(A-B) \cup (B-A)| = |A| + |B| - 2|A \cap B| = 26$ $|A| = 20$ $|(A-B) \cup (B-A)| = 20 + |B| - 2|A \cap B| = 26$ $|B| = 6 + 2|A \cap B|$ $|A \cap B| \geq 1$ $|B| \geq 6 + 2 = 8$
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
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Quote:
 Originally Posted by ketanco thanks and why do we subtract twice of intersection in the formula? is this a formula to memorize?
draw a diagram of

$(A-B) \cup (B-A)$

and you'll see why.

 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
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Quote:
 Originally Posted by SC007 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
Wolframalpha.com can probably handle those

Mathematica certainly can

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