Insert ⊆ or s in each blank to make the resulting statement true. ∅ ____ {1, 4, 6, 8}

Key Concepts

Set Notation

Set notation is a mathematical language used to describe collections of objects, known as sets. The symbols used, such as '∅' for the empty set and '{1, 4, 6, 8}' for a set containing specific elements, help convey relationships between different sets. Understanding how to read and interpret these symbols is crucial for solving problems involving sets.

Subset

A subset is a set where all elements are contained within another set. The notation 'A ⊆ B' indicates that set A is a subset of set B, meaning every element of A is also an element of B. The empty set '∅' is a unique subset of every set, as it contains no elements and thus satisfies the subset condition for any set.

Empty Set

The empty set, denoted as '∅', is a fundamental concept in set theory representing a set with no elements. It plays a critical role in various mathematical contexts, including the definition of subsets and the concept of union and intersection. Recognizing that the empty set is a subset of any set is essential for understanding relationships between sets.