Thread: 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:

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

∩ i∈lAi = ?
∪ i∈lAi = ?

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∈lAi = ?
∪ i∈lAi = ?

Use the given notation. You have to determine:

and you know
so you have to determine:

Can you complete?

Originally Posted by Siron

Use the given notation. You have to determine:

and you know
so you have to determine:

Can you complete?

No I can't ... don't really understand where you are going to ...

Originally Posted by iwan1981

No I can't ... don't really understand where you are going to ...

@iwan1981
Do you understand that .

If you do tell us what are.

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

@ Plato:
Isn't 0 also a multiple? For example:

Originally Posted by Siron

@ Plato:
Isn't 0 also a multiple of all sets? For example:

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.

Originally Posted by Plato

@iwan1981
Do you understand that .

If you do tell us what are.

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

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

Right?

Originally Posted by iwan1981

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

Correct.
Now

Originally Posted by Plato

Correct.
Now

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?

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?

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!