Insert ⊆ or s in each blank to make the resulting statement true. {2, 4, 6} ____ {2, 3, 4, 5, 6}

Verified step by step guidance

1. Identify the relationship between the two sets: {2, 4, 6} and {2, 3, 4, 5, 6}.
2. Check if every element of the first set {2, 4, 6} is also an element of the second set {2, 3, 4, 5, 6}.
3. Since 2, 4, and 6 are all present in the second set, the first set is a subset of the second set.
4. The symbol for subset is $\subseteq$.
5. Therefore, the correct symbol to insert is $\subseteq$, making the statement {2, 4, 6} $\subseteq$ {2, 3, 4, 5, 6} true.

Key Concepts

Set Notation

Set notation is a mathematical language used to describe collections of objects, known as elements. In this context, sets are represented by curly braces, and elements are listed within them. Understanding how to read and interpret set notation is crucial for determining relationships between sets, such as subset and superset.

Subset (⊆)

A subset is a set where all its elements are also contained within another set. The notation A ⊆ B indicates that set A is a subset of set B. For example, if A = {2, 4, 6} and B = {2, 3, 4, 5, 6}, A is a subset of B because every element in A is also found in B.

Superset (s)

A superset is the opposite of a subset, indicating that a set contains all elements of another set. The notation A s B means that set A is a superset of set B. In the given example, if B = {2, 3, 4, 5, 6}, then B is a superset of A = {2, 4, 6} because it includes all elements of A.