# problem solving with Venn diagrams

I'm doing revision for Venn diagrams and sets. There is one exercise which I cant figure out how to place certain numbers which are shared between sets U, O and P in a Venn Diagram. This question involve using two circles (sorry If I dont name it correctly I'm just starting self-learning math as adult.)

This is question.

$U = \{$Whole numbers from $0$ to $15\}$

$O = \{$Odd numbers from $0$ to$15\}$

$P = \{$Prime numbers between $0$ and $15\}$

Represents the sets on Venn Diagram.

$$U = { 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}$$ $$O = { 1,3,5,7,9,11,13,15}$$ $$P = { 2,3,5,7,11,13}$$

The shared numbers between sets U, O and P are: $$UOP = { 3,5,7,11,13}$$

The numbers which are shared between sets U and O are: $$UO = {0,1,9,15}$$

The numbers which are between sets U and P are: $$UP = {2}$$

The numbers that are just in set U are :

$$U = { 4,6,8,10,12,14}$$

The problem I'm having is how to display UOP sets numbers on Venn Diagram. Thanks

• There's an error:: $O$ does not contain $0$. What you denote UOP is the intersection $U\cap O\cap P$. Note that both $O$ and $P$ are subsets of $U$. Commented Jul 16, 2018 at 21:41
• Thank you for spoting the mistake. Commented Jul 16, 2018 at 21:59
• You could draw $U$ as a rectangle with $O$ and $P$ as intersecting circles inside it, if I understand what you are asking. Commented Jul 16, 2018 at 22:20
• Yes I know this, but those numbers suppose to be within intersection between O and P or rather on the boarders of those two sets. This is where I'm confuse. Sorry for not explaning well enough. Commented Jul 16, 2018 at 22:43