Questions: If all the elements of set A are also elements of set B, then set A is a(n) of set B.

Solution Steps

To determine the appropriate word or phrase to fill in the blank, we need to understand the relationship between sets. If all elements of set A are also elements of set B, then set A is a subset of set B.

Given two sets \( A \) and \( B \), if all elements of \( A \) are also elements of \( B \), we denote this relationship as \( A \subseteq B \). This means that set \( A \) is a subset of set \( B \).

In the example provided, we have:

• \( A = \{1, 2, 3\} \)
• \( B = \{1, 2, 3, 4, 5\} \)

We can see that every element in set \( A \) is indeed present in set \( B \).

Since all elements of \( A \) are contained within \( B \), we conclude that \( A \) is a subset of \( B \).

Final Answer