Originally Posted by

**Kalovale**
No, and no. You didn't see the change in the quantifier from existential to universial (namely, from "there exists a problem" to "all problems").

Also, it is OR. You're negating the AND statement, by De Morgans, you get an OR. Everything needs to be negated (sure you can skip steps, but that makes it confusing and hard to follow). ~(for all) = (there exists), ~AND = OR, ~(at least) = at most.

Short of being technical, I could just make sense of it intuitively:

Is (1) **[no problem was solved by at least three girls]** sufficient to establish that (2) **[a problem that was solved by at least three girls and at least three boys] is false**? Why yes. The same applies for (3) **[no problem was solved by at least three boys]**. (1) and (3) are each individually sufficient for the truth of ~(2). Therefore in order for (2) to be true, both of them have to be false.

And **[no problem was solved by at least three girls/boys]** is logically equivalent to **[All problems were solved with at most 2 girls/boys]**.

EDIT: Oh man, that markdown.

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