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Universal emptiness: what set is a subset of every set?

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Final answer:

The empty set, denoted by ∅ or {}, is a subset of every set because it contains no elements and therefore can be considered a part of all sets in set theory.

Step-by-step explanation:

The set that is a subset of every set is known as the empty set or null set, often denoted by the symbol ∅ or {}. It is a fundamental concept in set theory, a branch of mathematics that deals with the study of collections of objects. The empty set is unique in that it contains no elements, yet it serves as a basis for building more complex mathematical structures. For any given set, the empty set is always a subset because there are no elements in the empty set to contradict this relationship. For instance,

if we have a set A = {1, 2, 3}, the empty set ∅ is a subset of A since there are no elements in the empty set that are not in A.

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