Universal set question.

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March 19th 2010, 06:19 PM
jvignacio

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!
March 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: $\{x:3\mathrel{\vert} x\}$ .
March 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: $\{x:3\mathrel{\vert} x\}$ .

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,

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

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!
March 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.
March 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 $\overline{B} = \{1,2,3,4,5,6,7,8,12 \}$ correct?
March 20th 2010, 07:03 AM
Plato

Quote:

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.
March 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!
March 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 $\overline{A \cup C} \cup \overline{C}$ ? what would go first if its something like this? the $\overline{A \cup C}$ ?

thanks!
March 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.