# Consider a binary operation $\ast$ on the set $$\{1, 2, 3, 4, 5\}$$ given by the following multiplication table (Table 1.2). \begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix} (i) Compute $(2*3)*4$ and $2*(3*4)$

## 1 Answer

Toolbox:
• To compare two binary operations we write the corresponding operation table and compare each entry in the table.
From the table, $2 \ast 3 = 1 \rightarrow (2 \ast 3) \ast 4 = 1 \ast4 = 1$
Similarly, $2 \ast (3 \ast 4) = 2 \ast (1) = 1$.
answered Mar 20, 2013

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