Given: \( S = \{2, (1,4)\} \)

Here, the set \(S\) has two elements:

• The number \(2\)
• The ordered pair \((1,4)\)

Hence, \(|S| = 2\).

Formula: The number of elements in the power set of a set having \(n\) elements is \(2^n\).

\[ |P(S)| = 2^{|S|} = 2^2 = 4 \]

✅ Therefore, the number of elements in \(P(S)\) is 4.