Step 1: Write the electronic configurations.
\(_{63}\)Eu\(^{2+}\) - [Xe] 4f\(^7\) 6s\(^0\)
\(_{64}\)Gd\(^{3+}\) - [Xe] 4f\(^7\) 5d\(^0\) 6s\(^0\)
\(_{63}\)Eu\(^{3+}\) - [Xe] 4f\(^6\) 6s\(^0\)
\(_{65}\)Tb\(^{3+}\) - [Xe] 4f\(^8\) 6s\(^0\)
\(_{62}\)Sm\(^{2+}\) - [Xe] 4f\(^6\) 6s\(^0\)
Step 2: Identify the ions with 4f\(^7\) configuration.
From the electronic configurations, we can see that Eu\(^{2+}\) and Gd\(^{3+}\) have 4f\(^7\) configurations.
Step 3: Select the correct option.
Therefore, the correct answer is (A) and (B) only.
Let \( A = \{-3, -2, -1, 0, 1, 2, 3\} \). A relation \( R \) is defined such that \( xRy \) if \( y = \max(x, 1) \). The number of elements required to make it reflexive is \( l \), the number of elements required to make it symmetric is \( m \), and the number of elements in the relation \( R \) is \( n \). Then the value of \( l + m + n \) is equal to: