To determine the common elements between the sets \( A \) and \( B \), we need to find their intersection. Intersecting two sets involves identifying the elements that are present in both sets.
Given:
[tex]\[ A = \{1, 2, 5\} \][/tex]
[tex]\[ B = \{2, 3, 4\} \][/tex]
The intersection of sets \( A \) and \( B \) is formed by finding the elements that are common to both sets.
Step-by-step process:
1. List the elements of set \( A \): \{1, 2, 5\}
2. List the elements of set \( B \): \{2, 3, 4\}
3. Identify the elements that appear in both sets.
- The element \( 1 \) is in set \( A \) but not in set \( B \).
- The element \( 2 \) is in both set \( A \) and set \( B \).
- The element \( 5 \) is in set \( A \) but not in set \( B \).
- The element \( 3 \) is in set \( B \) but not in set \( A \).
- The element \( 4 \) is in set \( B \) but not in set \( A \).
After evaluating the elements, we find that the only element common to both sets \( A \) and \( B \) is \( 2 \).
Hence, the set of common elements (the intersection) is:
[tex]\[ A \cap B = \{2\} \][/tex]
So, the common subset made from sets \( A \) and \( B \) is:
[tex]\[ \{2\} \][/tex]
