Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To solve this problem, we need to understand the logical structure described by the statement: "If \( x \Rightarrow y \) and \( y \Rightarrow z \), then \( x \Rightarrow z \)".
Let's break it down:
1. Implication:
- \( x \Rightarrow y \) means "if \( x \) then \( y \)"
- \( y \Rightarrow z \) means "if \( y \) then \( z \)"
2. Transitivity:
- If \( x \) implies \( y \), and \( y \) implies \( z \), then it logically follows that \( x \) implies \( z \).
The structure of this logic is a classic example of a syllogism. A syllogism is a form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises). Each premise shares a common term with the conclusion, which in this case are the logical implications linking \( x \), \( y \), and \( z \).
To clarify why the other options are incorrect:
- Inverse statement: This refers to negating both the hypothesis and the conclusion of an implication (i.e., if \( x \Rightarrow y \), the inverse is \( \neg x \Rightarrow \neg y \)).
- Converse statement: This swaps the hypothesis and conclusion of an implication (i.e., if \( x \Rightarrow y \), the converse is \( y \Rightarrow x \)).
- Contrapositive statement: This refers to negating and swapping the hypothesis and conclusion (i.e., if \( x \Rightarrow y \), the contrapositive is \( \neg y \Rightarrow \neg x \)).
Since none of these terms correctly describe the given logical structure, the best term is indeed "syllogism".
Hence, the correct answer is:
C. A syllogism
Let's break it down:
1. Implication:
- \( x \Rightarrow y \) means "if \( x \) then \( y \)"
- \( y \Rightarrow z \) means "if \( y \) then \( z \)"
2. Transitivity:
- If \( x \) implies \( y \), and \( y \) implies \( z \), then it logically follows that \( x \) implies \( z \).
The structure of this logic is a classic example of a syllogism. A syllogism is a form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises). Each premise shares a common term with the conclusion, which in this case are the logical implications linking \( x \), \( y \), and \( z \).
To clarify why the other options are incorrect:
- Inverse statement: This refers to negating both the hypothesis and the conclusion of an implication (i.e., if \( x \Rightarrow y \), the inverse is \( \neg x \Rightarrow \neg y \)).
- Converse statement: This swaps the hypothesis and conclusion of an implication (i.e., if \( x \Rightarrow y \), the converse is \( y \Rightarrow x \)).
- Contrapositive statement: This refers to negating and swapping the hypothesis and conclusion (i.e., if \( x \Rightarrow y \), the contrapositive is \( \neg y \Rightarrow \neg x \)).
Since none of these terms correctly describe the given logical structure, the best term is indeed "syllogism".
Hence, the correct answer is:
C. A syllogism
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.