# How to Write Set A if Set B is a Factor of it

• anonymous007
In summary, the conversation is about sets of natural numbers and determining if an element in one set is a factor of an element in another set. Set C is defined as the elements in set A that are factors of the elements in set B. The notation used is C={a in A : \exists b in B such that b|a}.
anonymous007
Hi, I was just wondering, if I have a set (denoted by A)of natural numbers, 1,2,3,4,5,6,7,8,9,10 and each element(1,2,3,4,5,6,7,8,9,10) in the set is denoted by a,b,c,d,e,f,g,h,i,j

and set B is the natural numbers 2 and 3

How would I say that if an element in set B is a factor of an elemetn in set A, then take that element in A( which B is a factor of) and and place it into a set C

for example, since the elemetents 2,3,4,6,9,10 in set A are multiples of the elements in set B
then set C is the elements 2,3,4,6,9,10

C={a in A : $$\exists$$ b in B such that b|a}. Is that what you meant?

## 1. How do I write Set A if Set B is a factor of it?

To write Set A if Set B is a factor of it, you can use the notation A = nB, where n is any integer. This means that every element in Set B will be a factor of every element in Set A.

## 2. What does it mean for one set to be a factor of another?

A set being a factor of another means that all the elements in the first set are also elements in the second set. In other words, the first set is a subset of the second set.

## 3. Can Set B be a factor of Set A if Set A is not a subset of Set B?

No, in order for a set to be a factor of another set, the first set must be a subset of the second set. This means that all the elements in the first set must also be elements in the second set.

## 4. Are there any other ways to write Set A if Set B is a factor of it?

Yes, there are other ways to write Set A if Set B is a factor of it. Some examples include using the notation A = mB, where m is any real number, or writing A = {x | x ∈ B}, which means that A is the set of all elements in B.

## 5. Is it possible for both Set A and Set B to be factors of each other?

Yes, it is possible for both Set A and Set B to be factors of each other. This would mean that both sets are subsets of each other and have the same elements. In other words, they are equal sets.

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