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Jeff Shreeves November 15th, 2018 12:01 PM

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?

mathman November 15th, 2018 12:55 PM

How many teachers?????

topsquark November 15th, 2018 02:56 PM

Quote:

Originally Posted by Jeff Shreeves (Post 602413)
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 (Post 602414)
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. :dance:

-Dan

Jeff Shreeves November 15th, 2018 09:51 PM

Quote:

Originally Posted by Jeff Shreeves (Post 602413)
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

Jeff Shreeves November 15th, 2018 10:28 PM

Guys please help with the question

romsek November 15th, 2018 11:23 PM

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

$|\neg P| = 36$
$|\neg X| = 70$
$|P \cap X| = 61$
$|(P-X) \cup (X-P)| = 68$

$|(P-X) \cup (X-P)| = |P| + |X| - 2|P \cap X|$

$N-|P| = 36$
$|P| = N-36$
$N-|X| = 70$
$|X| = N-70$

$(N-36) + (N-70) - 2(61) = 68$

$2N = 296$

$N = 148$

skipjack November 16th, 2018 03:15 AM

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.


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