Answer to Question #29026 in Calculus for maria

Question

Hello expert ,can you tell me any reason that empty set is the subset of every set.

Answer 1

By the definition of subset, the empty set is a subset of any set A, as every element x of empty set belongs to A. If it is not true that every element of empty set is in A, there must be at least one element of empty set that is not present in A. Since there are no elements of empty set at all, there is no element of empty set that is not in A. Hence every element of empty set is in A, and empty set is a subset of A.