# Thread: Sets: Given 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}, define 𝑨𝒎 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

1. ## Sets: Given 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}, define 𝑨𝒎 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

Hi,

can someone help me with understanding this:

Let 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}.
For any positive integer 𝒎 we define the set 𝑨𝒎 by𝐴𝑚 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

So I created set A = {-infinite,...,-1,0,1,2,...,10}
But I'm stuck with Am.

Is this right solution?

A1 = {1}
A2 = {1,2}
A3 = {1,2,3}
...
?
Thanks

2. Originally Posted by kironet
Let 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}.
For any positive integer 𝒎 we define the set 𝑨𝒎 by𝐴𝑚 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

So I created set A = {-infinite,...,-1,0,1,2,...,10}
But I'm stuck with Am.

Is this right solution?

A1 = {1}
A2 = {1,2}
A3 = {1,2,3}
...
?
I dunno. What did they tell you to do with "A" and "Am"? Are you supposed to list out the elements of all such sets "Am"? Or something else?

Thank you!

3. Originally Posted by kironet
Hi,

can someone help me with understanding this:

Let 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}.
For any positive integer 𝒎 we define the set 𝑨𝒎 by𝐴𝑚 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

So I created set A = {-infinite,...,-1,0,1,2,...,10}
But I'm stuck with Am.

Is this right solution?

A1 = {1}
A2 = {1,2}
A3 = {1,2,3}
...
?
Thanks
Your "A" is wrong; you seem to have missed that 1 ≤ n.

If you were told to write out the first several sets Am, when you say that A3 = {1,2,3}, you are saying that 1, 2, and 3 are all factors of 3 (since m is 3, and you need to list every element of A that is a factor of m). Is that right?

4. Hi, sorry this is the full question:

Let 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}.
For any positive integer 𝒎 we define the set 𝑨𝒎 by𝐴𝑚 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

Give the sets 𝐴3, 𝐴6 and 𝐴8 explicitly in terms of their elements.

After research I came up with this:

A = {1,2,...,10}
A3={1,3}
A6={1,2,3,6}
A8={1,2,4,8}

Does it look correct?

5. Originally Posted by kironet
Hi, sorry this is the full question:

Let 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}.
For any positive integer 𝒎 we define the set 𝑨𝒎 by𝐴𝑚 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

Give the sets 𝐴3, 𝐴6 and 𝐴8 explicitly in terms of their elements.

After research I came up with this:

A = {1,2,...,10}
A3={1,3}
A6={1,2,3,6}
A8={1,2,4,8}

Does it look correct?
Well, let's check it:

A = {1,2,...,10} -- these are the numbers such that 1 ≤ 𝒏 ≤ 𝟏0 -- yes
A3={1,3} -- these are the numbers in A such that each is a factor of 3 -- yes
A6={1,2,3,6} -- these are the numbers in A such that each is a factor of 6 -- yes
A8={1,2,4,8} -- these are the numbers in A such that each is a factor of 8 -- yes

Good job!

I find it helpful to think of the condition in "set builder notation" as a test that an entity has to pass in order to be allowed into the set -- a membership exam, if you like. So we give each element that test (and make sure that no one else would pass it), and we see that your answer is right.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•