(c)
$Ca(OH)_{2} + Ca\left( HCO_{3} \right)_{2}\ \rightarrow 2CaCO_{3} \downarrow \ + H_{2}O\$
(A)
Temporary hardness of water is removed by $Ca(OH)_{2}.$ It converts bicarbonates into insoluble calcium and magnesium carbonate which are removed by filtration.
$Ca(OH)_{2}\ \ \ \ + \ \ \ \ \ Na_{2}CO_{3} \longrightarrow \ \ \ \ CaCO_{3}\ \ \ \ \ \ + \ \ \ \ \ 2NaOH$
$\ \ \ \ \ \ \ A$ sodium carbonate caustic soda
$Ca(OH)_{2} + 2CO_{2}\ \rightarrow Ca\left( HCO_{3} \right)_{2}$
$(A)$ calcium bicarbonate
(cloudy)