A thermal power plant operates on a regenerative cycle with a single open feed water heater, as shown in the figure. For the state points shown, the specific enthalpies are: $${h_1} = 2800\,\,kJ/kg$$ and $${h_2} = 200\,\,kJ/kg$$. The bleed to the feed-water heater is $$20\% $$ of the boiler steam generation rate. The specific enthalpy at state $$3$$ is

Which combination of the following statements is correct?

The incorporation of re-heater in a steam power plant.

$$P:$$ always increases the thermal efficiency of the plant.
$$Q:$$ always increases the dryness function of steam at condenser inlet.
$$R:$$ always increases the mean temperature of heat addition
$$S:$$ always increases the specific work output.

Determine the correctness or otherwise of the following Assertion $$(a)$$ and the Reason$$(r).$$

Assertion(A): In a power plant working on a Rankine cycle, the regenerative feed water heating improves the efficiency of the steam turbine.

Reason(R): The regenerative feed water heating raises the average temperature of heat addition in the Rankine cycle.

Assertion (A): Condenser is an essential equipment in a steam power plant.

Reason(R): For the same mass flow rate and the same pressure rise, a water pump requires substantially less power than a steam compressor.