Let 0 and 1 denote the null and unit elements of a Boolean algebra B. The following four functions with argument in B and values in B are of fundamental importance in Boolean algebra. They are: the null function, defined by 0x = 0; the unit function, defined by 1x = 1; the identity function j, defined by jx = x, and the complementary function c, defined by the rule, ex is the complement of x. These four functions, 0, 1, j, c, form a tri-operational algebra in the sense of Karl Menger.
Proceedings of the Iowa Academy of Science
©1946 Iowa Academy of Science, Inc.
Chittenden, E. W.
"On the Characterization of the Algebra of Four Fundamental Boolean Functions,"
Proceedings of the Iowa Academy of Science, 53(1), 247-248.
Available at: https://scholarworks.uni.edu/pias/vol53/iss1/29