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# 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} (iii) Compute $(2 \ast 3) \ast (4 \ast 5)$

Toolbox:
• To compare two binary operations we write the corresponding operation table and compare each entry in the table.
From the table, $(2 \ast 3) = 1$ and $(4 \ast 5) = 1$.
Therefore $(2 \ast 3) \ast (4 \ast 5) = 1 \ast 1 = 1$.