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 February 24th, 2018, 12:44 PM #1 Member     Joined: Jun 2017 From: Lima, Peru Posts: 52 Thanks: 1 Math Focus: Calculus How do I find the least number of elements in a series of sets? I need help with this elementary set problem it states as follows: In a toddler's room there are 120 toys, 95 of them uses batteries, 86 have wheels, 94 are red color, 110 are made of plastic, 100 emit sound. How many of the toys share all the characteristics? Initially I thought upon building up a series of equations such as $\textrm{I defined u as the unknown set which has all the elements}$ $\displaystyle b+u=95$ $\displaystyle w+u=86$ and so on, but then I thought that I can't assume that all the ones that uses batteries also includes the others characteristics. Since I have not good knowledge of set theory I'd like to get some help with this with a method that can be easy to follow. Thanks in advance.
 February 24th, 2018, 02:38 PM #2 Global Moderator   Joined: May 2007 Posts: 6,641 Thanks: 625 There is not enough information. The maximum is 86. The minimum is a lot smaller.
 February 27th, 2018, 06:23 AM #3 Global Moderator   Joined: Dec 2006 Posts: 19,957 Thanks: 1844 The minimum number of toys that share all 5 characteristics is 5, as explained on math.stackexchange (question 2665013).

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