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Chapter 1: Problem 15

Which of the following statements can be derived from the other four statements? A. The smallest orbit is not planet A's or B's. B. Planet D has the largest orbit. C. Planet \(\mathrm{C}\) is not in an orbit next to planet E's or D's. D. Planet \(\mathrm{E}\) is closest to the sun. E. None of the statements above can be derived.

Short Answer

Expert verified
The statement that can be derived from the other four is Statement E: None of the above can be derived.

Step by step solution

01

Analyze statement A

Statement A says that the smallest orbit is not planet A's or B's. This cannot be deduced from the other statements as there is no other information about the orbits of planets A and B in the remaining statements.
02

Analyze Statement B

Statement B, which states that planet D has the largest orbit, also cannot be deduced from the other statements. There is no other information about planet D's orbit in the remaining statements.
03

Analyze Statement C

Statement C can't be deduced from the other statements as well. It states that planet C is not in an orbit next to E's or D's, but other statements provide no information about the relative positions of C, D, or E's orbits.
04

Analyze Statement D

Statement D claims that planet E is closest to the sun. This might be a potential candidate, because being closest to the sun means that planet E would have the smallest orbit. But there is no other statement supporting this claim.
05

Analyze Statement E

Statement E - None of the statements can be derived, fits with all the above analysis. None of the statements A through D can be derived from the others. Therefore, statement E can be considered derived from statements A through D.

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