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By definition an empty set cannot have any elements, otherwise it would not be empty!

Think of a set as a container (like a box). The members of the set are those things inside it; there can be lots of things in a box, or just one, or none - when there are no items in the box it is empty, hence a set with no members is the empty set.

A subset is made by taking some of the items from the set (or box) and putting them into another: many, one or no items can be taken to make the subset. It is always possible to take no items from a set, thus the empty set is a subset of ALL sets.

For example, consider the set of people drinking coffee with 6 members: there are 3 latte drinkers, 1 cappuccino drinker, 2 espressos drinkers; various subsets can be made, eg:

* those drinking lattes (3 members);

* those drinking cappuccinos (1 member); or

* those drinking tea (no members: the empty set - tea is not coffee and the original set is those who drink coffee).

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Q: Why can an empty set have an element and a subset?
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