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 November 15th, 2018, 01:01 PM #1 Newbie   Joined: Nov 2018 From: Indianapolis Posts: 15 Thanks: 0 Set Theory Question Hard set theory question please help ASAP Out of a group of boys, 36 don’t have PS4, 70 don’t have an XBOX, whilst 61 have both a PS4 and an XBOX. If 68 boys have one or other machine, but not both, then how many teachers are in the group? Last edited by Jeff Shreeves; November 15th, 2018 at 01:14 PM.
 November 15th, 2018, 01:55 PM #2 Global Moderator   Joined: May 2007 Posts: 6,642 Thanks: 626 How many teachers?????
November 15th, 2018, 03:56 PM   #3
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Quote:
 Originally Posted by Jeff Shreeves Hard set theory question please help ASAP Out of a group of boys, 36 don’t have PS4, 70 don’t have an XBOX, whilst 61 have both a PS4 and an XBOX. If 68 boys have one or other machine, but not both, then how many teachers are in the group?
Quote:
 Originally Posted by mathman How many teachers?????
Well, one teacher took away 36 PS4s because the students weren't paying attention and the second teacher took away 70 XBOXs because the students stuck gum under their desks. So two teachers.

-Dan

November 15th, 2018, 10:51 PM   #4
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Quote:
 Originally Posted by Jeff Shreeves Hard set theory question please help ASAP Out of a group of boys, 36 don’t have PS4, 70 don’t have an XBOX, whilst 61 have both a PS4 and an XBOX. If 68 boys have one or other machine, but not both, then how many teachers are in the group?
Sorry I meant boys not teachers

 November 15th, 2018, 11:28 PM #5 Newbie   Joined: Nov 2018 From: Indianapolis Posts: 15 Thanks: 0 Guys please help with the question
 November 16th, 2018, 12:23 AM #6 Senior Member     Joined: Sep 2015 From: USA Posts: 2,203 Thanks: 1157 Let $N$ be the total number of boys let $P$ be the set of boys that have a PS4 let $X$ be the set of boys that have an Xbox we are given that $|\neg P| = 36$ $|\neg X| = 70$ $|P \cap X| = 61$ $|(P-X) \cup (X-P)| = 68$ $|(P-X) \cup (X-P)| = |P| + |X| - 2|P \cap X|$ $N-|P| = 36$ $|P| = N-36$ $N-|X| = 70$ $|X| = N-70$ $(N-36) + (N-70) - 2(61) = 68$ $2N = 296$ $N = 148$ Thanks from Jeff Shreeves
 November 16th, 2018, 04:15 AM #7 Global Moderator   Joined: Dec 2006 Posts: 19,986 Thanks: 1853 As 36 + 70 = 68 + 2 × number of boys with neither machine, 19 boys have neither machine. Hence total number of boys = 61 + 68 + 19 = 148. Thanks from Jeff Shreeves

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