Is it valid to proved the relationship among three parameter: hardness, conductivity and TDS by refers to this link ? http://www.globalw.com/support/hardness.html
The total hardness is divided into two parts, the first is the temporary hardness which is mentioned in your answer, and the second is the permanent hardness represented by the remaining positive and negative ions. Their total concentration represents total hardness.
Electrical conductivity is directly related to total dissolved solids. it is almost 65-75% of EC. TH is directly related to Ca, Mg and HCO3. These all included in TDS.