Inclusion Exclusion

[Sillysidley]

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

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...

BTW, it's spelled "complement", not "compliment".

[Sillysidley]

Oh well.
All you really need to do is draw a Venn Diagram Don't worry, I did it using the Inclusion Exclusion Property.

[Sillysidley]

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.

[Sillysidley]

Ok I figured them all out, using a Venn Diagram

I hate Venn Diagrams. I just solved the last one NOT using a venn diagram.
I wonder if you can make venn diagrams in ...

[Scion]

5 times 3 times 2 us 30 count by 30 to 1000

[Sillysidley]

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:

Originally Posted by somedude

You just divide 1000 by 30 and round down.