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

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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}.
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anonymous007
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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
 
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C={a in A : [tex]\exists[/tex] 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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