Consider the following statements regarding a first order system with a proportional \((\mathrm{P})\) controller which exhibits an offset to a step input.

In order to reduce the offset, it is necessary to

1. increase the gain of the \(\mathrm{P}\).

2. add derivative mode and increase gain of \(\mathrm{P}\).

3. add integral mode.

Of these statements:
(a) 1, 2 and 3 are correct
(b) 1 and 2 are correct
(c) 2 and 3 are correct
(d) 1 and 3 are correct.