Consider a binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table.

(i) Compute (2 * 3) * 4 and 2 * (3 * 4)

(ii) Is * commutative?

(iii) Compute (2 * 3) * (4 * 5).

(Hint: use the following table)

*	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

Consider a binary operation $\ast$ on set{1,2,3,4,5} given by the following multiplication table:
(iii)Compute $(2\ast 3)\times (4\ast 5)$
$\begin{array}{cccccc}\ast & 1& 2& 3& 4& 5\\ 1& 1& 1& 1& 1& 1\\ 2& 1& 2& 1& 2& 1\\ 3& 1& 1& 3& 1& 1\\ 4& 1& 2& 1& 4& 1\\ 5& 1& 1& 1& 1& 5\end{array}$

Complete the following table:

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

$\begin{array}{cccccc}\ast & 1& 2& 3& 4& 5\\ 1& 1& 1& 1& 1& 1\\ 2& 1& 2& 1& 2& 1\\ 3& 1& 1& 3& 1& 1\\ 4& 1& 2& 1& 4& 1\\ 5& 1& 1& 1& 1& 5\end{array}$

(ii) Is $\ast$ commutative?

$\begin{array}{cccccc}\ast & 1& 2& 3& 4& 5\\ 1& 1& 1& 1& 1& 1\\ 2& 1& 2& 1& 2& 1\\ 3& 1& 1& 3& 1& 1\\ 4& 1& 2& 1& 4& 1\\ 5& 1& 1& 1& 1& 5\end{array}$

(iii)Compute $(2\ast 3)\times \left(4ast5\right)$
$\begin{array}{cccccc}\ast & 1& 2& 3& 4& 5\\ 1& 1& 1& 1& 1& 1\\ 2& 1& 2& 1& 2& 1\\ 3& 1& 1& 3& 1& 1\\ 4& 1& 2& 1& 4& 1\\ 5& 1& 1& 1& 1& 5\end{array}$

Question 3(a)

Catherine threw a dice 40 times and noted the number appearing each time as shown below:
Make a table and enter the data using tally marks. Find the number that appeared the minimum number of times.

Question 3(b)

Catherine threw a dice 40 times and noted the number appearing each time as shown below:
Make a table and enter the data using tally marks. Find the number that appeared the maximum number of times.