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 Probability and Statistics Basic Probability and Statistics Math Forum

 November 14th, 2018, 08:22 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, 10:52 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,549 Thanks: 1399 $A \cap B \neq \emptyset$ $|A \cup B | = 17 = |A| + |B| - |A \cap B|$ $2^{|A \cap B|} = |A-B| = |A| - |A \cap B|$ $|A| - |A \cap B| = 17 - |B|$ $2^{|A \cap B|} = 17 - |B|$ $|B| = 17 - 2^{|A \cap B|}$ $|A \cap B|=4 \Rightarrow |B|=1$ 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. Thanks from ketanco November 15th, 2018, 12:34 AM   #3
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Quote:
 Originally Posted by romsek $A \cap B \neq \emptyset$ $|A \cup B | = 17 = |A| + |B| - |A \cap B|$ $2^{|A \cap B|} = |A-B| = |A| - |A \cap B|$ $|A| - |A \cap B| = 17 - |B|$ $2^{|A \cap B|} = 17 - |B|$ $|B| = 17 - 2^{|A \cap B|}$ $|A \cap B|=4 \Rightarrow |B|=1$ 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.
thanks and by the way how to write the symbols as you wrote here? November 15th, 2018, 01:19 AM   #4
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Quote:
 Originally Posted by ketanco thanks and by the way how to write the symbols as you wrote here?
the board supports LaTex

a quick cheat sheet is here November 15th, 2018, 03:15 AM   #5
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 Originally Posted by romsek the board supports LaTex a quick cheat sheet is here
so let me test: to write alpha, i must write slash and then the word?
\alpha

well i couldnt do it
i mean how do you write those symbols in here... November 15th, 2018, 03:47 AM   #6
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Quote:
 Originally Posted by ketanco so let me test: to write alpha, i must write slash and then the word? \alpha well i couldnt do it i mean how do you write those symbols in here...
You have to type it inside "math" tags (or equivalently \$). $\alpha$ gives$\displaystyle \alpha\$

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