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Subset and proper subset of a set

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As we know, a set is just a collection of objects that are similar in some way, like a gaggle of geese, pride of lions, or an army of ants. To further classify our world, we can create subsets from a larger set. Let's consider the idea of a subset for our discussion.

Give an example of a subset and a proper subset. Explain the difference between a subset and proper subset.

Can any set be a proper subset of itself? Give an example of why or why not.

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Solution Summary

The notions of a subset and a proper subset of a set are examined and illustrated.

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Set A is a subset of a set B if every element of A is also an element of B. This idea formalizes the notion of being a part of a whole.

A proper subset is defined as follows:

Set A is a proper subset of a set B if two conditions are met:
1) A is a subset of B.
2) A is not equal to B.

The reason for that definition is in ...

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