A water softening apparatus connectable to a tub, the water softening apparatus having an air brake assembly and a regeneration tank and configured to soften wash water being supplied from the tub, wherein the air brake assembly comprises: a water supply valve allowing wash water to be introduced therethrough; an ion exchange tank accommodating an ion exchange resin therein, wherein the ion exchange tank is provided at an inside of the air brake assembly; a plurality of valves (150, 160, 170) installed on a first path allowing wash water being introduced through the water supply valve to flow toward the ion exchange tank; and a supply water storage tank provided at the inside of the air brake assembly so as to be located at an upper side of the ion exchange tank and configured to store wash water being introduced through the water supply valve, wherein the regeneration tank is connected to the air brake assembly and accommodates regeneration material configured to purify the ion exchange resin; wherein the plurality of valves (150, 160, 170) comprises: a first valve configured to control a flow of the wash water being introduced through the water supply valve toward the supply water storage tank; a second valve configured to control a flow of the wash water being introduced through the water supply valve toward the regeneration tank; and a third valve configured to control a flow of the wash water being introduced through the water supply valve toward the ion exchange tank, wherein when the wash water is supplied to the supply water storage tank, the first valve is switched on, and the second valve and the third valve are switched off; and when the wash water stored in the supply water storage tank is discharged to the ion exchange tank, the first valve and the third valve are switched on, and the second valve is switched off. a water supply valve allowing wash water to be introduced therethrough; an ion exchange tank accommodating an ion exchange resin therein, wherein the ion exchange tank is provided at an inside of the air brake assembly; a plurality of valves (150, 160, 170) installed on a first path allowing wash water being introduced through the water supply valve to flow toward the ion exchange tank; and a supply water storage tank provided at the inside of the air brake assembly so as to be located at an upper side of the ion exchange tank and configured to store wash water being introduced through the water supply valve, wherein the regeneration tank is connected to the air brake assembly and accommodates regeneration material configured to purify the ion exchange resin; wherein the plurality of valves (150, 160, 170) comprises: a first valve configured to control a flow of the wash water being introduced through the water supply valve toward the supply water storage tank; a second valve configured to control a flow of the wash water being introduced through the water supply valve toward the regeneration tank; and a third valve configured to control a flow of the wash water being introduced through the water supply valve toward the ion exchange tank, wherein when the wash water is supplied to the supply water storage tank, the first valve is switched on, and the second valve and the third valve are switched off; and when the wash water stored in the supply water storage tank is discharged to the ion exchange tank, the first valve and the third valve are switched on, and the second valve is switched off. a first valve configured to control a flow of the wash water being introduced through the water supply valve toward the supply water storage tank; a second valve configured to control a flow of the wash water being introduced through the water supply valve toward the regeneration tank; and a third valve configured to control a flow of the wash water being introduced through the water supply valve toward the ion exchange tank, wherein when the wash water is supplied to the supply water storage tank, the first valve is switched on, and the second valve and the third valve are switched off; and when the wash water stored in the supply water storage tank is discharged to the ion exchange tank, the first valve and the third valve are switched on, and the second valve is switched off.