The complete products of a Boolean algebra of subsets generated by a set {A_k}_(k = 1)^p of cardinal number p are the 2^p Boolean functions B_1 B_2 ...B_p congruent B_1 intersection B_2 intersection ... intersection B_p, where each B_k may equal A_k or its complement A^__k. For example, the 2^3 = 8 complete products of A = {A_1, A_2, A_3} are A_1 A_2 A_3, A_1 A_2 A^__3, A_1 A^__2 A_3, A^__1 A_2 A_3, A_1 A^__2 A^__3, A^__1 A_2 A^__3, A^__1 A^__2 A_3, A^__1 A^__2 A^__3. Each Boolean function has a unique representation (up to order) as a union of complete products.

Boolean function | conjunction