Could you explain your reasons? I think my slides and paper are correct, and that your proposed change would be wrong. The point is that (s union t) has size at least n, just in case there is a way of allocating the three parts of the Venn diagram with i,j,k so as to realize the three clauses. Certainly, if the right-hand side holds as I’ve described it, then of course, (s union t) will have at least size n, and conversely, if s union t has size at least n, then there will be some i+j+k=n realizing the desired pattern.
So I don’t regard this as a “typo”. But perhaps I’m missing something?

(Meanwhile, I have corrected the link; thanks very much for that.)

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