# Universal set question.

• Mar 19th 2010, 06:19 PM
jvignacio
Universal set question.
Hey guys,
So in a universal set that $\displaystyle x$ are all natural numbers and $\displaystyle x \le 12$
does $\displaystyle C = \{ x | 3|x \}$ mean all positive integers divisible by 3?
So in this case it would be 3, 6, 9, 12 ?

thanks!
• Mar 20th 2010, 01:47 AM
emakarov
I would say so.

To avoid confusing notation, it is possible to replace the first vertical bar with a colon: $\displaystyle \{x:3\mathrel{\vert} x\}$.
• Mar 20th 2010, 06:08 AM
jvignacio
Quote:

Originally Posted by emakarov
I would say so.

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

thanks for that idea and reply.

Also if:
in a universal set that http://www.mathhelpforum.com/math-he...155c67a6-1.gif are all natural numbers and http://www.mathhelpforum.com/math-he...d6fd9e79-1.gif,

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

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

Would I start with the brackets $\displaystyle (A\cup \overline{B})$ then get that result and work out $\displaystyle [RESULT] \cap C$ ? Also i cant figure out $\displaystyle \overline{B}$ from the B set... any help? thank you!
• Mar 20th 2010, 06:18 AM
emakarov
Quote:

Would I start with the brackets http://www.mathhelpforum.com/math-he...20e7ed0b-1.gif then get that result and work out http://www.mathhelpforum.com/math-he...f0faa959-1.gif ?
Yes, of course.

Quote:

Also i cant figure out http://www.mathhelpforum.com/math-he...e0c94b31-1.gif from the B set.
http://www.mathhelpforum.com/math-he...e0c94b31-1.gif denotes the complement of B, i.e., all elements of the universal set that are not in B.
• Mar 20th 2010, 06:25 AM
jvignacio
Quote:

Originally Posted by emakarov
Yes, of course.

http://www.mathhelpforum.com/math-he...e0c94b31-1.gif denotes the complement of B, i.e., all elements of the universal set that are not in B.

Ah right so in this case $\displaystyle \overline{B} = \{1,2,3,4,5,6,7,8,12 \}$ correct?
• Mar 20th 2010, 07:03 AM
Plato
Quote:

Originally Posted by jvignacio
Ah right so in this case $\displaystyle \overline{B} = \{1,2,3,4,5,6,7,8,12 \}$ correct?

That is correct if your text material does not include 0 as a natural number.
• Mar 20th 2010, 08:18 AM
jvignacio
Quote:

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!
• Mar 21st 2010, 02:34 AM
jvignacio
Quote:

Originally Posted by emakarov
Yes, of course.

http://www.mathhelpforum.com/math-he...e0c94b31-1.gif denotes the complement of B, i.e., all elements of the universal set that are not in B.

hey there, what about something like$\displaystyle \overline{A \cup C} \cup \overline{C}$ ? what would go first if its something like this? the $\displaystyle \overline{A \cup C}$?

thanks!
• Mar 21st 2010, 06:43 AM
emakarov
Quote:

what would go first if its something like this? the http://www.mathhelpforum.com/math-he...4fc5de9c-1.gif?
Yes.