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D Theorem: A group of 7 kids have a total of 20 chocolate bars. Then at least one of the kids has fewer than three chocolate bars. A proof by contradiction of the theorem starts by assuming which fact? All the kids have at least three chocolate bars. There is a kid with more than three chocolate bars. There is a kid with at least three chocolate bars. O All the kids have more than three chocolate bars. Question 32 Theorem: There is no smallest positive rational number. A proof by contradiction of the theorem starts by assuming which fact? O Let r be the smallest positive real number. O Let r be an arbitrary positive rational number. O Letr be the smallest positive rational number. O Let r be the smallest rational number.
Theorem: For any real number x, x + (x - 512 5 In a proof by cases of the theorem, there are two cases. One of the cases is that x> 5. What is the other case? O X20 xs5 O x<0 O xzy O x<y x50 O x<5 Question 34 Ox<0 Theorem: For any real numbers, x and y, max(x, y) = (1/2) (x + y + x - yl). One of the cases in the proof of the theorem uses the assumptions that Ix-yl-x-y. Select the case that corresponds to this argument.
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