Question 5 - A-Level Maths

Exam Board	AQA
Module	Further AS Paper 2 Discrete (Further AS Paper 2 Discrete)
Year	2019
Session	June
Topic	Groups

Complete the Cayley table in Figure 1 for multiplication modulo 4 \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{dcf97b92-d067-41d4-89a6-ea5bab9ea4ff-08_761_1017_434_493}
\end{figure} 5
The set $S$ is defined as $$S = \{ a , b , c , d \}$$ Figure 2 shows an incomplete Cayley table for $S$ under the commutative binary operation • \begin{table}[h]
\captionsetup{labelformat=empty} \caption{Figure 2}
• $a$ $b$ $c$ $d$
$a$ $b$ $a$ $a$ $c$
$b$ $c$ $c$
$c$ $d$ $d$
$d$ $d$ $d$
\end{table} 5
1. Complete the Cayley table in Figure 2. 5
(ii) Determine whether the binary operation • is associative when acting on the elements of $S$. Fully justify your answer.