Consider a binary operation ∗ on set{1,2,3,4,5} given by the followi

1.	Consider a binary operation ∗ on set{1,2,3,4,5} given by the following multiplication table: (i)Compute (2∗3)∗4 and 2∗(3∗4) ∗12345111111212121311311412141511115 (ii) Is ∗ commutative? ∗12345111111212121311311412141511115 (iii)Compute (2∗3)×(4ast5) ∗12345111111212121311311412141511115
Answer» Consider a binary operation $$ on set{1,2,3,4,5} given by the following multiplication table: (i)Compute $(2 3) * 4$ and $2 * (3 * 4)$ $\begin{matrix} * & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$ (ii) Is $$ commutative? $\begin{matrix} & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$ (iii)Compute $(2 * 3) \times (4 a s t 5)$ $\begin{matrix} * & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$

Consider a binary operation ∗ on set{1,2,3,4,5} given by the following multiplication table: (i)Compute (2∗3)∗4 and 2∗(3∗4) ∗12345111111212121311311412141511115 (ii) Is ∗ commutative? ∗12345111111212121311311412141511115 (iii)Compute (2∗3)×(4ast5) ∗12345111111212121311311412141511115

Answer»

Consider a binary operation $*$ on set{1,2,3,4,5} given by the following multiplication table:
(i)Compute $(2 * 3) * 4$ and $2 * (3 * 4)$

$\begin{matrix} * & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$

(ii) Is $*$ commutative?

$\begin{matrix} * & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$

(iii)Compute $(2 * 3) \times (4 a s t 5)$
$\begin{matrix} * & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$

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