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Symbolically: Clear[s,a,b,c,d]; s={a,b,c,d}; uni@@s==Total[Map[-(-1)^Length[#]int@@#&,Rest[Subsets[s]],1]]/.int[q_]->q; uni[a,b,c,d] == a + b + c + d - int[a, b] - int[a, c] - int[a, d] - int[b, c] - int[b, d]-int[c,d] + int[a, b, c] + int[a, b, d] + int[a, c, d] + int[b, c, d] - int[a, b, c, d] Now, fill in ...


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y = 2*x - x^2; Plot[y, {x, 0, 2}] Yields: So the range is (0,1] because 1 is within the range because it happens at f(1)=1. 0 is not actually in the range, because 0 is not in the domain (because (0,2)). But 1 is definitely in the range, because 1 is definitely in the domain.



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