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Each of the species of a certain type of insect has at least one of five significant traits: A, B, C, D, and E. Furthermore, one study has determined that any species with Trait A has at least one of the Traits B and C. Another study has determined that any species with Trait C has at least one of the Traits D and E. And a third study has determined that any of the species with Trait B has Trait C. The results of each study are correct.
In addition to the relationship between Traits B and C that is stated explicitly with respect to the third study, the passage implies that any of the insects that has Trait X also has Trait Y. Select different options for X and for Y such that the following statement most accurately describes the passage.
A
B
C
D
E
| Passage Statement | Analysis & Implications |
| "Each species has at least one of five traits: A, B, C, D, and E" |
|
| "Any species with Trait A has at least one of Traits B and C" |
|
| "Any species with Trait C has at least one of Traits D and E" |
|
| "Any species with Trait B has Trait C" |
|
Let's trace through the logical chains:
We need to find X and Y where \(\mathrm{X} \rightarrow \mathrm{Y}\) is implied by the passage.
\(\mathrm{A} \rightarrow \mathrm{B}\)? No, \(\mathrm{A} \rightarrow (\mathrm{B} \text{ or } \mathrm{C})\), not necessarily B
\(\mathrm{A} \rightarrow \mathrm{C}\)? Yes! Whether A leads to B or C, we always get C
\(\mathrm{A} \rightarrow \mathrm{D}\)? No, \(\mathrm{A} \rightarrow \mathrm{C} \rightarrow (\mathrm{D} \text{ or } \mathrm{E})\), could be E instead
\(\mathrm{A} \rightarrow \mathrm{E}\)? No, same reasoning as above
\(\mathrm{B} \rightarrow \mathrm{D}\)? No, \(\mathrm{B} \rightarrow \mathrm{C} \rightarrow (\mathrm{D} \text{ or } \mathrm{E})\), could be E instead
\(\mathrm{B} \rightarrow \mathrm{E}\)? No, same reasoning as above
\(\mathrm{C} \rightarrow \mathrm{A}\)? No, nothing implies A must exist
\(\mathrm{D} \rightarrow \text{anything}\)? No implications given about D
\(\mathrm{E} \rightarrow \text{anything}\)? No implications given about E
Part 1 (X): A - This trait creates an implied relationship
Part 2 (Y): C - This is the trait that must follow from A
Let's confirm \(\mathrm{A} \rightarrow \mathrm{C}\):
This is the only additional guaranteed relationship we can derive from the given facts.