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Use Euler diagrams to determine whether the following argument is valid or invalid. All fish are cold blooded creatures. A trout is one of the cold blooded creatures. Therefore, a trout is one of the fish. Choose the correct answer below. Invalid Valid

Use Euler diagrams to determine whether the following argument is valid or invalid. All fish are cold blooded creatures. A trout is one of the cold blooded creatures. Therefore, a trout is one of the fish. Choose the correct answer below. Invalid Valid

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
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**Analyzing Arguments with Euler Diagrams** **Argument:** 1. All fish are cold-blooded creatures. 2. A trout is one of the cold-blooded creatures. 3. Therefore, a trout is one of the fish. **Task:** Use Euler diagrams to determine whether this argument is valid or invalid. **Explanation:** To analyze this argument, we can use Euler diagrams, which are visual representations of logical relationships. In this scenario, we have three categories: - Fish - Cold-blooded creatures - Trout 1. **Fish**: This category is entirely within the category of cold-blooded creatures. 2. **Cold-blooded Creatures**: This is a larger category that includes all fish. However, it also may include other animals that are not fish. The argument assumes that because a trout is a cold-blooded creature, it must also be a fish. However, the statement "a trout is one of the cold-blooded creatures" does not necessarily mean it is a fish, because cold-blooded creatures can include many other non-fish animals. **Conclusion:** The conclusion drawn in the argument ("Therefore, a trout is one of the fish") is not valid based solely on the premises provided. While a trout is indeed a fish, this argument does not logically prove that fact. **Choose the correct answer below:** - ⃝ Invalid - ⃝ Valid The correct choice is "Invalid" because the argument does not correctly establish that a trout must be a fish based solely on the premises given.
Transcribed Image Text:**Analyzing Arguments with Euler Diagrams** **Argument:** 1. All fish are cold-blooded creatures. 2. A trout is one of the cold-blooded creatures. 3. Therefore, a trout is one of the fish. **Task:** Use Euler diagrams to determine whether this argument is valid or invalid. **Explanation:** To analyze this argument, we can use Euler diagrams, which are visual representations of logical relationships. In this scenario, we have three categories: - Fish - Cold-blooded creatures - Trout 1. **Fish**: This category is entirely within the category of cold-blooded creatures. 2. **Cold-blooded Creatures**: This is a larger category that includes all fish. However, it also may include other animals that are not fish. The argument assumes that because a trout is a cold-blooded creature, it must also be a fish. However, the statement "a trout is one of the cold-blooded creatures" does not necessarily mean it is a fish, because cold-blooded creatures can include many other non-fish animals. **Conclusion:** The conclusion drawn in the argument ("Therefore, a trout is one of the fish") is not valid based solely on the premises provided. While a trout is indeed a fish, this argument does not logically prove that fact. **Choose the correct answer below:** - ⃝ Invalid - ⃝ Valid The correct choice is "Invalid" because the argument does not correctly establish that a trout must be a fish based solely on the premises given.
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