another set related question ...

Hi,

I am trying to understand this set related question:

===========================

Given the following sets:

*V* = { *n* ∈ ℤ|0 ≤ *n* ≤ 15}

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

and a list of 5 sets:

*A**i* = { *n *∈*V*|*n* is a multiple of *i*}, where all *i* ∈ *l*

(Notation: ∪ *i*∈ {1,2,3} *A**i* = *A*1 ∪ *A*2 ∪ *A*3 )

∩ *i*∈*lA**i* = ?

∪ *i*∈*lA**i* = ?

Answers:

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:

∩ *i*∈*lA**i* = ?

∪ *i*∈*lA**i* = ?

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?

Re: another set related question ...

Quote:

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 ...

Re: another set related question ...

Quote:

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.

Re: another set related question ...

@ Plato:

Isn't 0 also a multiple? For example:

$\displaystyle A_3=\{0,3,6,9,12,15\}$

Re: another set related question ...

Quote:

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.

Re: another set related question ...

Quote:

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?

Re: another set related question ...

Quote:

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

$\displaystyle \bigcap\limits_{i \in I} {A_i } = A_3 \cap A_4 \cap A_5 \cap A_6 \cap A_7 = ?$

Re: another set related question ...

Quote:

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?

Re: another set related question ...

Quote:

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?

Re: another set related question ...

Quote:

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? :-)

Re: another set related question ...