Notwithstanding any other provision of the general or public laws to the contrary, the property taxes owed for any real property in the city of Providence owned by an entity organized as a cooperative housing corporation within the meaning of chapter 6.1 of Title 7 shall be reduced by applying to the assessed value of that property all personal exemptions (including, for example, the homestead exemption and exemptions available to veterans, disabled veterans, elderly persons, former prisoners of war, and the blind) to which any shareholders of the corporation residing on the property would be entitled if they directly owned and occupied residential property in the city or town where the corporation’s property is located. In calculating the amount of any property tax reduction, the personal exemptions to which any resident shareholder is entitled shall not be applied to the portion of the common areas on the corporation’s property used for recreational or social purposes, such as game rooms, fitness facilities, dining rooms or theaters. The burden shall be on the corporation to demonstrate the extent to which any of its resident shareholders would qualify to receive the exemptions.