1 The following Cayley table is for a set \(\{ a , b , c , d \}\) under a suitable binary operation.
| \(a\) | \(b\) | \(c\) | \(d\) |
| \(a\) | \(b\) | | \(a\) | |
| \(b\) | | | | |
| \(c\) | | | \(c\) | |
| \(d\) | \(d\) | | | \(a\) |
- Given that the Latin square property holds for this Cayley table, complete it using the table supplied in the Printed Answer Booklet.
- Using your completed Cayley table, explain why the set does not form a group under the binary operation.