# Thread: another set related question ...

1. ## another set related question ...

Hi,

I am trying to understand this set related question:

===========================
Given the following sets:
V = { n |0n 15}

l = {3, 4, 5, 6, 7}

and a list of 5 sets:

Ai = { n V|n is a multiple of i}, where all i l
(Notation: i {1,2,3} Ai = A1 A2 A3 )

ilAi = ?
ilAi = ?

a. {11,13}
b. {3,4,5,6,7,8,9,10,12,14,15}
c. {0}
d. {1,2}
e. {0,3,4,5,6,7,8,9,10,12,14,15}
f. {0,1,11,13}
===========================

We need to determine what the answer is for:
ilAi = ?
ilAi = ?

2. ## Re: another set related question ...

Use the given notation. You have to determine:
$\displaystyle \cap i \in I, A_i = ...$
and you know $\displaystyle I=\{3,4,5,6,7\}$
so you have to determine:
$\displaystyle \cap i \in \{3,4,5,6,7 \}, A_i=A_3\cap ...$
Can you complete?

3. ## Re: another set related question ...

Originally Posted by Siron
Use the given notation. You have to determine:
$\displaystyle \cap i \in I, A_i = ...$
and you know $\displaystyle I=\{3,4,5,6,7\}$
so you have to determine:
$\displaystyle \cap i \in \{3,4,5,6,7 \}, A_i=A_3\cap ...$
Can you complete?
No I can't ... don't really understand where you are going to ...

4. ## Re: another set related question ...

Originally Posted by iwan1981
No I can't ... don't really understand where you are going to ...
@iwan1981
Do you understand that $\displaystyle A_3=\{0,3,6,9,12,15\}~\&~A_7=\{0,7,14\}~?$.

If you do tell us what $\displaystyle A_4,~A_5,~\&~A_6$ are.

If you do not then short of doing the question for you, I don't know how we can help you.

5. ## Re: another set related question ...

@ Plato:
Isn't 0 also a multiple? For example:
$\displaystyle A_3=\{0,3,6,9,12,15\}$

6. ## Re: another set related question ...

Originally Posted by Siron
@ Plato:
Isn't 0 also a multiple of all sets? For example:
$\displaystyle A_3=\{0,3,6,9,12,15\}$
Frankly, I do not know.
Do we consider 0 a multiple of 3? If so, then it should be there.
It appears as if we should include it.

7. ## Re: another set related question ...

Originally Posted by Plato
@iwan1981
Do you understand that $\displaystyle A_3=\{0,3,6,9,12,15\}~\&~A_7=\{0,7,14\}~?$.

If you do tell us what $\displaystyle A_4,~A_5,~\&~A_6$ are.

If you do not then short of doing the question for you, I don't know how we can help you.

$\displaystyle A_4,~A_5,~\&~A_6$

A4 = {0, 4, 8, 12}
A5 = {0, 5, 10, 15}
A6 = {0, 6, 12}

Right?

8. ## Re: another set related question ...

Originally Posted by iwan1981
$\displaystyle A_4,~A_5,~\&~A_6$
A4 = {0, 4, 8, 12}
A5 = {0, 5, 10, 15}
A6 = {0, 6, 12}
Right?
Correct.
Now
$\displaystyle \bigcap\limits_{i \in I} {A_i } = A_3 \cap A_4 \cap A_5 \cap A_6 \cap A_7 = ?$

9. ## Re: another set related question ...

Originally Posted by Plato
Correct.
Now
$\displaystyle \bigcap\limits_{i \in I} {A_i } = A_3 \cap A_4 \cap A_5 \cap A_6 \cap A_7 = ?$
A3 = {0, 3, 6, 9, 12, 15}
A4 = {0, 4, 8, 12}
A5 = {0, 5, 10, 15}
A6 = {0, 6, 12}
A6 = {0, 7, 14}

∩ means means the set that contains all those elements that A1, A2, A3, A4, A5, A6 and A7 have in common so this will be: c. {0}

Right?

10. ## Re: another set related question ...

Originally Posted by iwan1981
A3 = {0, 3, 6, 9, 12, 15}
A4 = {0, 4, 8, 12}
A5 = {0, 5, 10, 15}
A6 = {0, 6, 12}
A6 = {0, 7, 14}

∩ means means the set that contains all those elements that A1, A2, A3, A4, A5, A6 and A7 have in common so this will be: c. {0} Right?
Good.
Now what is the union?

11. ## Re: another set related question ...

Now what is the union?
The Union = ∪

∪ means that the set of those elements which are either in A1 or in A2 or in A3 or in A4 or in A5 or in A6 or in A7 , or in all of them.

So the Union is e. {0,3,4,5,6,7,8,9,10,12,14,15}

right? :-)

Correct!