Before revision: In vector logic the equivalence p≡q is represented by the following matrix: with and The Exclusive or is the negation of the equivalence, ¬(p≡q); it corresponds with the matrix given by with and NAND and NOR The matrices S and P correspond to the Sheffer (NAND) and the Peirce (NOR) operations, respectively:
After revision: Numerical examplesHere are numerical examples of some basic logical gates implemented as matrices for two different sets of 2-dimensional orthonormal vectors for s and n.Set 1:In this case the identity and negation operators are the identity and anti-diagonal identity matrices:,and the matrices for conjunction, dysjunction and implication arerespectively.In vector logic the equivalence p≡q is represented by the following matrix: with and The Exclusive or is the negation of the equivalence, ¬(p≡q); it corresponds with the matrix given by with and NAND and NOR The matrices S and P correspond to the Sheffer (NAND) and the Peirce (NOR) operations, respectively: