On diluting a solution of a weak electrolyte, which of the following is correct?

Dilution reduces the number of ions per unit volume, so conductivity $\kappa$ falls. Molar conductivity ${\Lambda }_m=\kappa /c$ refers to one mole of electrolyte; dilution raises the degree of dissociation $\alpha$, so ${\Lambda }_m$ rises (sharply for weak electrolytes).