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# Number of binary operations on the set $\{a, b\}$ are

$\begin{array}{1 1} 10 \\ 16 \\ 20 \\ 8 \end{array}$

The number binary operation defined by * from $\{(a,a)(a,b),(b,a),(b,b)\} \to \{a,b\}$ is $2^4=16$

edited Mar 20, 2013