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# Needs help in logic

A={2,3,4}
B={3,4,5,6}
U={1,2,3,4,5,6,7,8,9}

P(B\A)

Answer is
{0,{5},{6},{5,6}}

Dont know how it get that needs help. Thanks.
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mustish1
Asked:
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1 Solution

Commented:
See:  http://www.mathgoodies.com/lessons/vol6/conditional.html
for explanation on conditional probabilty...

Rule to use is:
P(B | A)  =   P(A and B)  /  P(A)
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Author Commented:
A={2,3,4}
B={3,4,5,6}
(A and B) = {2,3,4,5,6}

is this is correct. I am guessing here and means U.
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Author Commented:
I think B\A = {5, 6} because 5 and 6 are elements of B but not of A.
power set of {5, 6} means ?
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Author Commented:
The proper subsets of {5, 6} are {5} and {6} and then add in the empty set and the set itself.

i dont know if this is the way to do that.
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Commented:
I believe you are correct in your assumptions!  Thus you match the answer given in your original poser.
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Commented:
Um, it's not conditional probability. The problem is asking for the power set of A\B
A\B is the set of elements that are in A and not in B so {5,6} in this case. And then the power set is all the possible subsets you can create from that set so of course it would be the { {Ø} {5} {6} {5,6} }
As long as you mean empty set when you write {0} then your answer is correct. I would use the Ø character instead to avoid confusion (Hold the Alt key down and press 0216 on the keypad in Windows to get that character).
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Commented:
Sorry, of course in your question we had B\A (elements in B but not in A). I wrote A\B in the above post, but the definition is the same so don't let my typo confuse you.
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