Full Adder Circuit . Part I

A set is pair if: (Def.1) There exist sets x, y such that it = 〈x, y〉. Let us mention that every set which is pair is also non empty. Let x, y be sets. Observe that 〈x, y〉 is pair. Let us mention that there exists a set which is pair and there exists a set which is non pair. Let us observe that every natural number is non pair. A set has a pair if: (Def.2) There exists a pair set x such that x ∈ it. Note that every set which is empty has no pairs. Let x be a non pair set. Note that {x} has no pairs. Let y be a non pair set. Observe that {x, y} has no pairs. Let z be a non pair set. One can check that {x, y, z} has no pairs.