# Question Why is the empty set ∅ considered a subset of every set? > [!question]- Answer Choices > (A) Because it contains no elements that could violate the subset condition > (B) Because it is the smallest possible set > (C) Because every set must have at least one subset > (D) Because set theory defines it this way arbitrarily > (E) Because the empty set equals zero > [!solution]- Solution > To understand why ∅ ⊆ A for any set A, we need to recall the definition of subset: Set X is a subset of set Y if every element of X is also in Y. > >For the empty set ∅, this condition is vacuously true. Since ∅ has no elements, there are no elements in ∅ that could fail to be in A. In logical terms, the statement "for all x in ∅, x is in A" is true because there is no x in ∅ to serve as a counterexample. > This is not an arbitrary definition but follows from the logical structure of the subset definition when applied to a set with no elements. > > **Answer: (A)**