Inclusion Exclusion - XP Math - Forums

 XP Math - Forums Inclusion Exclusion

 04-27-2007 #1 Sillysidley   Join Date: Oct 2006 Posts: 822 Inclusion Exclusion Let U=(1,2,3..,1000) and let A2,A3, and A5 be the numbers that are divisible by 2,3, and 5 respectively. Find: a. The intersection of all 3 sets (I solved this already) b. The intersection of A2,A3, and the compliment of A5 c. The intersection of A2, the compliment ofA3, and A5. d. The intersection of the compliment of A2,A3, and A5 e. The intersection of A2, the compliment of A3, and the compliment of A5 __________________ . Last edited by Sillysidley; 04-27-2007 at 06:30 PM..
 04-28-2007 #2 Temperal Guest   Posts: n/a a) To solve this, we need to find all numbers x where 2a=x, 3b=x and 5c=x. These are all primes, so we could try multiplying. 2*3*5=30 4*3*5=60 6*3*5=90 8*3*5=120 We see a pattern here. Since it must end in 0 or 5, it must be even, and divisible by 3, this is easy. The intersection is I=(30,60,90,120,150...) all the way up to 1,000. Is it right, somedude? I'll do the rest later...
 04-28-2007 #3 Temperal Guest   Posts: n/a BTW, it's spelled "complement", not "compliment".
 04-28-2007 #4 Sillysidley   Join Date: Oct 2006 Posts: 822 Oh well. All you really need to do is draw a Venn Diagram Don't worry, I did it using the Inclusion Exclusion Property. __________________ .
04-28-2007   #5
Sillysidley

Join Date: Oct 2006
Posts: 822

Quote:
 Originally Posted by Archive a) To solve this, we need to find all numbers x where 2a=x, 3b=x and 5c=x. These are all primes, so we could try multiplying. 2*3*5=30 4*3*5=60 6*3*5=90 8*3*5=120 We see a pattern here. Since it must end in 0 or 5, it must be even, and divisible by 3, this is easy. The intersection is I=(30,60,90,120,150...) all the way up to 1,000. Is it right, somedude? I'll do the rest later...
You just divide 1000 by 30 and round down.
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 04-29-2007 #6 Sillysidley   Join Date: Oct 2006 Posts: 822 Ok I figured them all out, using a Venn Diagram __________________ .
 04-29-2007 #7 Temperal Guest   Posts: n/a I hate Venn Diagrams. I just solved the last one NOT using a venn diagram. I wonder if you can make venn diagrams in $\LaTeX$...
 05-01-2007 #8 Scion   Join Date: Nov 2006 Posts: 437 5 times 3 times 2 us 30 count by 30 to 1000 __________________
05-04-2007   #9
Sillysidley

Join Date: Oct 2006
Posts: 822

Quote:
 Originally Posted by redfirex well 33.33 thats not the answer though you never told us to round haha i beat you 1000/30 then knock off the remainder
Ahem:
Quote:
 Originally Posted by somedude You just divide 1000 by 30 and round down.
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