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From what I know, boolean operators are the likes of AND, OR, XOR, NOT, NAND and NOR. So does this mean that there are actually 6 distinct boolean operators that can take three inputs?

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marked as duplicate by Joey Zou, Daniel W. Farlow, Leucippus, Parcly Taxel, user99914 Aug 31 '16 at 6:57

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  • $\begingroup$ That helped a lot. Thanks! $\endgroup$ – user315656 Aug 31 '16 at 0:17
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Each operation you've listed takes two inputs, not three. Moreover, you've missed two: the "YES" operator (always outputs "true") and the "NO" operator (always outputs false).

Can you show that these are all the Boolean operations on two inputs that there are? HINT: Can you identify each Boolean operation on two inputs with a function from a four-element set to a two-element set? If so, how many of those are there?

This example should also suggest the general formula for how many Boolean operations of a given arity there are.

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