Statement A: On dilution, the equivalent as well molar conductivity of the solution increases.

Statement B: with dilution, the number of current carry­ing particles per ${\mathrm{cm}}^3$ increases.

On dilution, the number of current carrying particles per ${\mathrm{cm}}^3$ decreases and hence specific conductivity decreases. ${\mathrm{\Lambda }}_{\mathrm{eq}}$ and ${\mathrm{\Lambda }}_{\mathrm{m}}$ increase with dilution because ${\mathrm{\Lambda }}_{\mathrm{eq}}=$Specific conductivity x volume of solution containing 1 g eq. of the electrolyte 

and ${\mathrm{\Lambda }}_{\mathrm{m}}=$Specific conductivity x volume of solution containing 1 mole of the electrolyte and volume increases much more and hence decrease in specific conductivity.