a * b =
$ \begin{matrix} \text{a + b} & \text{if} & \text{a + b < 6} \\ \text{a + b - 6,} & \text{if} & \text{a + b }\geq6 \\ \end{matrix}$. Show that zero is the identity for this operation and each element 'a' of the set is, invertible with 6 – a, being the inverse of 'a'.Note: $\forall$ a $\in$ {0, 1, 2, 3, 4, 5}
$\therefore$ 0 is the identity for *.
Also,$\forall$ a $\in$ {0, 1, 2, 3, 4, 5}, a * (6 – a) = a + (6 – a) – 6= 0 (which is identity)
Each element ‘a’ of the set is invertible with (6 – a), being the inverse of ‘a’.Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
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