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 November 14th, 2018, 08:05 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 14th, 2018, 11:00 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,549 Thanks: 1399 $|(A-B) \cup (B-A)| = |A| + |B| - 2|A \cap B| = 26$ $|A| = 20$ $|(A-B) \cup (B-A)| = 20 + |B| - 2|A \cap B| = 26$ $|B| = 6 + 2|A \cap B|$ $|A \cap B| \geq 1$ $|B| \geq 6 + 2 = 8$ Thanks from ketanco November 15th, 2018, 12:41 AM   #3
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 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, 01:17 AM   #4
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 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, 09:32 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, 10:50 AM   #6
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 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 Tags elements, intersection, number, set Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post jroff419 Probability and Statistics 2 May 4th, 2017 09:14 PM Ganesh Ujwal Abstract Algebra 4 April 14th, 2015 10:48 AM fidanym Topology 4 October 28th, 2014 02:15 AM grigor Applied Math 0 March 25th, 2014 11:25 PM blondie16 Linear Algebra 1 April 28th, 2011 08:38 AM

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