Questions: Quiz: Biconditionals and Definitions CR Geometry A (GP) 24-25 / 2:Reasoning and Proof 1. Is the following statement a good definition? Why? A penny is a United States coin worth one cent. No, it is not. The statement is not precise. No, it is not. The statement is not reversible. Yes, it is. The statement is precise and reversible. Yes, it is. The statement is precise.

Quiz: Biconditionals and Definitions CR Geometry A (GP) 24-25 / 2:Reasoning and Proof 1. Is the following statement a good definition? Why? A penny is a United States coin worth one cent. No, it is not. The statement is not precise. No, it is not. The statement is not reversible. Yes, it is. The statement is precise and reversible. Yes, it is. The statement is precise.
Transcript text: Quiz: Biconditionals and Definitions CR Geometry A (GP) 24-25 / 2:Reasoning and Proof 1. Is the following statement a good definition? Why? A penny is a United States coin worth one cent. No, it is not. The statement is not precise. No, it is not. The statement is not reversible. Yes, it is. The statement is precise and reversible. Yes, it is. The statement is precise.
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Solution

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Solution Steps

Step 1: Analyze the Statement

The statement given is: "A penny is a United States coin worth one cent." To determine if this is a good definition, we need to check if it is both precise and reversible.

Step 2: Check for Precision

A precise definition should clearly describe the object or concept without ambiguity. The statement "A penny is a United States coin worth one cent" is precise because it specifies the exact value and origin of the coin.

Step 3: Check for Reversibility

A reversible definition means that if you reverse the statement, it should still hold true. In this case, reversing the statement would be: "A United States coin worth one cent is a penny." This reversed statement is also true, as the only U.S. coin worth exactly one cent is a penny.

Final Answer

The statement is both precise and reversible, making it a good definition. Therefore, the answer is:

\[ \boxed{\text{Yes, it is. The statement is precise and reversible.}} \]

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