Answer. The addition of washing soda removes the calcium and magnesium ions as the insoluble calcium and magnesium carbonates, respectively. As a result permanent hardness of water removes.
Na2CO3(aq) + CaSO4(aq) CaCO3(s) + NaSO4(aq)
Na2CO3(aq) + MgSO4(aq) MgCO3(s) + Na2SO4(aq)