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Every kid knows the phrase, [kid sing-songy] "Trick or treat!" But have you

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ever stopped to wonder — what kind of _"or"_ is that, exactly?

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Let's start with the obvious interpretation: Two circles—two children. Orange means

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treats, gray means tricks. This is inclusive OR: If any child

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knocks, everyone gets candy. Only an empty porch gets tricks.

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[quickly] [chuckles] Is this how Venn diagrams work? Not at all!

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But hey, it's Halloween—logic gets to wear a costume, too.

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[title] Trick AND Treat Both children must show up together, or

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nobody gets treats. [sarcastic] One lonely kid? Sorry, that's a trick.

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[title] Trick XOR Treat This house rewards exactly one visitor.

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Too few or too many, and everyone gets tricked.

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These three behaviors cover most houses on the block.

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But De Morgan's laws hint at something more... a

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theoretical complement to each. A spooky, inverted reflection.

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[spooky] What cursed operations lurk in the penumbra of reason?

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Let's face our fears and venture into the dark.

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[title] Trick NOR Treat: the Halloween hater. This neighbor

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only gives treats when nobody visits. [quick laugh] The

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only winning move is not to play.

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[title] Trick NAND Treat: NOT-AND—the reverse psychology neighbor. This

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house gives treats to everyone... except pairs. Come alone?

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Treats. Don't come at all? ...[chuckles] Also Treats. Come

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together? [mischievous] That's the only way to get tricked.

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[title] Trick XNOR Treat: the conformity enforcer—XOR inverted. This neighbor

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rewards matching behavior. Both kids visit, or both stay home?

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Treats. Just one kid? [judgmental] That's a trick.

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These bottom-row operations are... deeply strange. They're the

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kinds of houses you'd skip entirely. But mathematically?

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They're just as valid as the classics.

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So the next time a child asks [kid sing-songy]

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"trick or treat?", you now have the mathematically correct

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response: [annoying high-pitched nasal pedantic] "That depends—which logical operator

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are you implementing?" [quick laugh] ...though I wouldn't recommend

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it if you don't want your house getting egged.