4 Elements of the set \(\{ p , q , r , s , t \}\) are combined according to the operation table shown below.
| \(p\) | \(q\) | \(r\) | \(s\) | \(t\) |
| \(p\) | \(t\) | \(s\) | \(p\) | \(r\) | \(q\) |
| \(q\) | \(s\) | \(p\) | \(q\) | \(t\) | \(r\) |
| \(r\) | \(p\) | \(q\) | \(r\) | \(s\) | \(t\) |
| \(s\) | \(r\) | \(t\) | \(s\) | \(q\) | \(p\) |
| \(t\) | \(q\) | \(r\) | \(t\) | \(p\) | \(s\) |
- Verify that \(q ( s t ) = ( q s ) t\).
- Assuming that the associative property holds for all elements, prove that the set \(\{ p , q , r , s , t \}\), with the operation table shown, forms a group \(G\).
- A multiplicative group \(H\) is isomorphic to the group \(G\). The identity element of \(H\) is \(e\) and another element is \(d\). Write down the elements of \(H\) in terms of \(e\) and \(d\).