Step 1: First, determine the sets \( A \) and \( B \):
Step 2: The number of relations from set \( A \) to set \( B \) is given by the total number of subsets of the Cartesian product \( A \times B \). The number of elements in \( A \times B \) is:
\[ |A| \times |B| = 3 \times 3 = 9 \]
Step 3: The number of relations is the number of subsets of \( A \times B \), which is \( 2^9 \), since each pair in \( A \times B \) can either be included in or excluded from the relation. Thus, the correct answer is:
\[ 2^9 \]
\( \text{M} \xrightarrow{\text{CH}_3\text{MgBr}} \text{N} + \text{CH}_4 \uparrow \xrightarrow{\text{H}^+} \text{CH}_3\text{COCH}_2\text{COCH}_3 \)
Identify the ion having 4f\(^6\) electronic configuration.