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The pairs of matrices shown in the following boxes are twins. This is shorthand for the fact, that their rows are Zhegalkin twins. (Compare Zhegalkin matrix.)

The left side of each pair shows the truth tables of s. (Compare these 16×16 matrices, which also show the arguments.)

Some of them are unusual, and have unusual names: SAND (a.k.a. minimal negation operator) could be called all but one. Its reflection SNOR could be called no but one. The name XOR is used for the. The reflection of not XOR is called XAND. (Because the reflection of not OR is AND.) GAND is SAND extended by AND. Its reflection GNOR is SNOR extended by not OR. In ESAND and OSAND this extension happens only for an even or odd number of arguments. Their reflections are ESNOR and OSNOR. EQ makes sense as generalization of the, and is true if all arguments have the same truth value (but not if there are no arguments).

The right side of each pair is a lower. Its entries are part of the, which is the twin of not OR.

Each of these triangles is symmetric to another one (in two cases to itself). Only the triangle rows are symmetric (not the matrix rows). Pairs with symmetric triangles are in the same box, e.g.: XOR / OSAND, SNOR / OSNOR

 Some triangles are relative complements in the Sierpinski triangle: TRUE / OR, AND / EQ, GNOR / SNOR, OSNOR / ESNOR