So I recently learned that you can derive all four of the propositional logic operators (~, V, &, →) from Nand alone.(adsbygoogle = window.adsbygoogle || []).push({});

As I have understood it, so long as you have negation, and one of the other operators, you can derive the rest. Like P → Q can be defined as ~P V Q.

However, I learned that if you start with the Nand (Not and) operator, you can derive all four. I'll use ' N ' to designate Nand.

The truth table for Nand being

P Q | P N Q

T T | F

F T | T

T F | T

F F | T

~P := P N P

P & Q := (P N Q) N (P N Q)

P V Q := (P N P) N (Q N Q)

P -> Q := (P N Q) N (Q N Q)

Isn't that cool?

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# Derive all four propositional logic operators from nand

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