- #1
JC2000
- 186
- 16
- Homework Statement
- A survey shows that ##63 %## Americans like cheese where as ##76 %## like apples. If ##x %## like both, find ##x##.
- Relevant Equations
- Since ##A \cap B \subset A## and ## A \cap B \subset B## :
##n(A \cap B) \leq n(A)## and ##n(A \cap B) \leq n(B)##
i.e ##n(A \cap B) \leq 63##
Also, ##n(A\cap B ) \geq 39## since ##n(A\cap B) = n(A)+ n(B)-n(A\cup B)## but ##n(A\cup B) \leq 100##
Thus : ## 39 \leq x \leq 63##
My Question :
1.Why are the inequalities considered? Why not simply use ##n(A\cap B) = n(A)+ n(B)-n(A\cup B)## to get ## n(A\cap B) = 39## ?
2. The way I interpret this is : If the set for people liking cheese was to be a subset of the set for people who like apples then the most number of people to like both would be 63. But I still fail to understand why the minimum value should be 39 (Why : ##P(A) + P(B) - P(A \cup B) < 1##)?
1.Why are the inequalities considered? Why not simply use ##n(A\cap B) = n(A)+ n(B)-n(A\cup B)## to get ## n(A\cap B) = 39## ?
2. The way I interpret this is : If the set for people liking cheese was to be a subset of the set for people who like apples then the most number of people to like both would be 63. But I still fail to understand why the minimum value should be 39 (Why : ##P(A) + P(B) - P(A \cup B) < 1##)?
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