Question:
Write the total number of binary operations on a set consisting of two elements.
Concept:
If a set has \( n \) elements, then the number of binary operations on the set is:
\[ n^{n^2} \]
Solution:
Given set has 2 elements, so \( n = 2 \)
\[ \text{Number of binary operations} = 2^{2^2} \]
\[ = 2^4 = 16 \]
Final Answer:
\[ \boxed{16} \]