Question

write the converse of this statement and decide whether it is true or false. then, select the correct answer. if shelley lives in arizona, then she lives in the united states. a b c d e if arizona is in the united states, then shelley lives there; true

Explanation:

1. Recall the definition of the converse of a conditional statement: For a statement "If \( p \), then \( q \)", the converse is "If \( q \), then \( p \)".
2. Apply this to the given statement: Original statement: \( p \): Shelley lives in Arizona; \( q \): she lives in the United States. Converse: If \( q \) (Shelley lives in the United States), then \( p \) (she lives in Arizona).
3. Evaluate the truth value: There are many states in the US, so living in the US does not imply living in Arizona. Thus, the converse is false. The option in the image misinterprets the hypothesis and conclusion, so it is incorrect.

Answer:

The converse of the statement "If Shelley lives in Arizona, then she lives in the United States" is "If Shelley lives in the United States, then she lives in Arizona". This converse is false. (Note: The option provided in the image is incorrect. The correct converse should switch the hypothesis and conclusion of the original conditional statement. The original hypothesis is "Shelley lives in Arizona" and the conclusion is "she lives in the United States". So the converse should have hypothesis "she lives in the United States" and conclusion "Shelley lives in Arizona", which is false because someone can live in the US but not in Arizona.)