# Math Help - Universal set question.

1. ## Universal set question.

Hey guys,
So in a universal set that $x$ are all natural numbers and $x \le 12$
does $C = \{ x | 3|x \}$ mean all positive integers divisible by 3?
So in this case it would be 3, 6, 9, 12 ?

thanks!

2. I would say so.

To avoid confusing notation, it is possible to replace the first vertical bar with a colon: $\{x:3\mathrel{\vert} x\}$.

3. Originally Posted by emakarov
I would say so.

To avoid confusing notation, it is possible to replace the first vertical bar with a colon: $\{x:3\mathrel{\vert} x\}$.
thanks for that idea and reply.

Also if:
in a universal set that are all natural numbers and ,

$A= \{ 3,4,5,6,7,8,9,10 \}$
$B = \{ 9, 10, 11 \}$
$C = \{ 3,6,9,12 \}$

whats $(A\cup \overline{B}) \cap C =$ ?

Would I start with the brackets $(A\cup \overline{B})$ then get that result and work out $[RESULT] \cap C$ ? Also i cant figure out $\overline{B}$ from the B set... any help? thank you!

4. Would I start with the brackets then get that result and work out ?
Yes, of course.

Also i cant figure out from the B set.
denotes the complement of B, i.e., all elements of the universal set that are not in B.

5. Originally Posted by emakarov
Yes, of course.

denotes the complement of B, i.e., all elements of the universal set that are not in B.
Ah right so in this case $\overline{B} = \{1,2,3,4,5,6,7,8,12 \}$ correct?

6. Originally Posted by jvignacio
Ah right so in this case $\overline{B} = \{1,2,3,4,5,6,7,8,12 \}$ correct?
That is correct if your text material does not include 0 as a natural number.

7. Originally Posted by Plato
That is correct if your text material does not include 0 as a natural number.
Your right, I should find out.

Thanks!

8. Originally Posted by emakarov
Yes, of course.

denotes the complement of B, i.e., all elements of the universal set that are not in B.
hey there, what about something like $\overline{A \cup C} \cup \overline{C}$ ? what would go first if its something like this? the $\overline{A \cup C}$?

thanks!

9. what would go first if its something like this? the ?
Yes.