Lefty not realizing the comic says trans are violent criminals
(media.kotakuinaction2.win)
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The first one is using the Mathematician's Yes. Technically, you can answer yes to "Are you a boy or a girl?" and be correct. Of course, doing so is admitting that you fall under the binary one way or the other, so they really just played themselves.
The "or" we use in English often translates into XOR in math/logic. So "boy or girl" becomes "boy XOR girl", which is just a tautology since it's always going to be one or the other but never both.
You can answer "yes" to it only if you are already working within Gender Theory, which is an issue all by itself.
What? There are only two options, and answering yes is just saying "Yes, I am Male or Female."
"Yes" is only possible under Gender Theory, as in to refer to both. The question presumes an exclusive distinction. You are either male or female. Saying "yes" dismisses the presumption in the first place.
The problem people in this discussion are having is that English isn't as precise as math and logic. XOR is usually the math/logic equivalent of the English "or". "boy XOR girl" is always going to be true since it's always one or the other and never both.