A nanodomain is an object studied in the field of mathematical stereotopodynamics. A nanodomain may be doubly- Euclidean, or not, and it may be skew-differentiable, or not. You are given a list of statements concerning a nanodomain X; some of these statements are logically equivalent, that is, they are just different ways of saying the same thing. Group the statements into logically equivalent sets and enter your answer below as a list of sets separated by commas. Syntax advice: For example, if you think that statements 1,2,3 are logically equivalent; and statements 4,5,6,7 are logically equivalent (but different from 1,2,3); and statement 8 is different from all the others; then your answer should be {1,2,3}, {4,5,6,7}, {8} The order of your sets, and the order of the elements in each set, are not important.

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A nanodomain is an object studied in the field of mathematical stereotopodynamics. A nanodomain may be doubly-
Euclidean, or not, and it may be skew-differentiable, or not. You are given a list of statements concerning a
nanodomain X; some of these statements are logically equivalent, that is, they are just different ways of saying the
same thing.
Group the statements into logically equivalent sets and enter your answer below as a list of sets separated by
commas.
Syntax advice: For example, if you think that statements 1,2,3 are logically equivalent; and statements 4,5,6,7 are
logically equivalent (but different from 1,2,3); and statement 8 is different from all the others; then your answer
should be
{1,2,3}, {4,5,6,7}, {8}
The order of your sets, and the order of the elements in each set, are not important.
(1) X is doubly-Euclidean, or X is not skew-differentiable
(2) X is skew-differentiable if X is doubly-Euclidean
(3) X is doubly-Euclidean and X is not skew-differentiable
(4) X is doubly-Euclidean, or X is skew-differentiable
(5) if X is not skew-differentiable, then X is doubly-Euclidean
(6) X is doubly-Euclidean only if X is skew-differentiable
(7) if X is skew-differentiable, then X is doubly-Euclidean
(8) if X is doubly-Euclidean, then X is skew-differentiable
Transcribed Image Text:A nanodomain is an object studied in the field of mathematical stereotopodynamics. A nanodomain may be doubly- Euclidean, or not, and it may be skew-differentiable, or not. You are given a list of statements concerning a nanodomain X; some of these statements are logically equivalent, that is, they are just different ways of saying the same thing. Group the statements into logically equivalent sets and enter your answer below as a list of sets separated by commas. Syntax advice: For example, if you think that statements 1,2,3 are logically equivalent; and statements 4,5,6,7 are logically equivalent (but different from 1,2,3); and statement 8 is different from all the others; then your answer should be {1,2,3}, {4,5,6,7}, {8} The order of your sets, and the order of the elements in each set, are not important. (1) X is doubly-Euclidean, or X is not skew-differentiable (2) X is skew-differentiable if X is doubly-Euclidean (3) X is doubly-Euclidean and X is not skew-differentiable (4) X is doubly-Euclidean, or X is skew-differentiable (5) if X is not skew-differentiable, then X is doubly-Euclidean (6) X is doubly-Euclidean only if X is skew-differentiable (7) if X is skew-differentiable, then X is doubly-Euclidean (8) if X is doubly-Euclidean, then X is skew-differentiable
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