- #1
bomba923
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If a set "C" can contain any subset of a set "A", then is "A" itself a subset of (or equal to) "C" ??
Is Set A a Subset of Set C as well?
- Thread starter bomba923
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In summary, a subset is a set that contains all the elements of another set. To determine if one set is a subset of another, you need to compare the elements of both sets. The size of a set does not affect whether it is a subset or not. If a set has elements that are not present in the larger set, it is not considered a subset. However, a set is always considered a subset of itself.
- #2
HallsofIvy
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Do you mean by "contain" "has as a subset"? If that is the case, then the answer is "yes". If C has every (proper) subset of A as a subset, then, in particular, it has every singleton set as a subset and so contains every element of A.
- #3
bomba923
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Thanks -- just what I needed to know 
FAQ: Is Set A a Subset of Set C as well?
1. What is a subset?
A subset is a set that contains all the elements of another set. In other words, all the elements in the subset are also present in the larger set.
2. How do you determine if Set A is a subset of Set C?
To determine if Set A is a subset of Set C, you need to compare the elements of both sets. If all the elements in Set A are also present in Set C, then Set A is a subset of Set C.
3. Can Set A be a subset of Set C if they have different sizes?
Yes, the size or number of elements in a set does not affect whether it is a subset or not. As long as all the elements in Set A are also present in Set C, it is considered a subset.
4. What happens if Set A has some elements that are not present in Set C?
If Set A has elements that are not present in Set C, then Set A is not a subset of Set C. In order for a set to be a subset, all its elements must be present in the larger set.
5. Can one set be a subset of itself?
Yes, a set is always considered a subset of itself. This is because all the elements in the set are also present in the same set.