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November 14th, 2018, 09:05 AM   #1
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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 ?
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November 15th, 2018, 12:00 AM   #2
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$|(A-B) \cup (B-A)| = |A| + |B| - 2|A \cap B| = 26$

$|A| = 20$

$|(A-B) \cup (B-A)| = 20 + |B| - 2|A \cap B| = 26$

$|B| = 6 + 2|A \cap B|$

$|A \cap B| \geq 1$

$|B| \geq 6 + 2 = 8$
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November 15th, 2018, 01:41 AM   #3
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Quote:
Originally Posted by romsek View Post
$|(A-B) \cup (B-A)| = |A| + |B| - 2|A \cap B| = 26$

$|A| = 20$

$|(A-B) \cup (B-A)| = 20 + |B| - 2|A \cap B| = 26$

$|B| = 6 + 2|A \cap B|$

$|A \cap B| \geq 1$

$|B| \geq 6 + 2 = 8$
thanks and why do we subtract twice of intersection in the formula? is this a formula to memorize?
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November 15th, 2018, 02:17 AM   #4
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Quote:
Originally Posted by ketanco View Post
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.
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December 4th, 2018, 10:32 AM   #5
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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
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December 4th, 2018, 11:50 AM   #6
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Quote:
Originally Posted by SC007 View Post
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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