(a) Property is not subject to property tax if the property:
(1) is owned by a nonprofit historical society, museum, or academy, the purposes of which are solely to study the history of or to maintain and preserve historic homes, places, and personal property for the use and benefit of the public; and
(2) is actually used exclusively for the purposes of any of these organizations.
(b) Up to 15 acres of property is not subject to property tax if the property:
(1) is owned by a nonprofit organization for the purpose of maintaining a commemorative park or site for a monument to the veterans of the armed services of:
(i) the United States; or
(ii) the Confederate States of America; and
(2) is actually used exclusively for the purposes of these organizations.