What is trivial subset?

Answer 1

The trivial subsets of a set are those subsets which can be found without knowing the contents of the set.

The empty set has one trivial subset: the empty set.

Every nonempty set S has two distinct trivial subsets: S and the empty set.

Explanation:

This is due to the following two facts which follow from the definition of subset:

Fact 1: Every set is a subset of itself.

Fact 2: The empty set is subset of every set.

The definition of subset says that if every element of A is also a member of B then A is a subset of B. If A is the empty set then every element of A (all 0 of them) are members of B trivially. If A = B then A is a subset of B because each element of A is a member of A trivially.