Question 5 - A-Level Maths

Exam Board	AQA
Module	Further AS Paper 2 Discrete (Further AS Paper 2 Discrete)
Year	2023
Session	June
Topic	Groups

The set $S$ is defined as $S = \{ 0,1,2,3,4,5 \}$ 5
1. State the identity element of $S$ under the operation multiplication modulo 6 5
(ii) An element $g$ of a set is said to be self-inverse under a binary operation * if $$g * g = e$$ where $e$ is the identity element of the set. Find all the self-inverse elements in $S$ under the operation multiplication modulo 6
5
$\quad$ The set $T$ is defined as $$T = \{ a , b , c \}$$ Figure 1 shows a partially completed Cayley table for $T$ under the commutative binary operation - \begin{table}[h]
\captionsetup{labelformat=empty} \caption{Figure 1}
- $a$ $b$ c
$a$ $a$ c b
$b$ $b$ $а$
c c
\end{table} 5
1. Complete the Cayley table in Figure 1 5
(ii) Prove that is not associative when acting on the elements of $T$