Final answer:
To write the inverse of the conditional statement "If I live in Charleston, then I live in South Carolina," change it to "If I do not live in Charleston, then I do not live in South Carolina." The inverse negates both the hypothesis and the conclusion of the original conditional statement.
Step-by-step explanation:
The question you've asked pertains to the concept of the inverse of a conditional statement in mathematical logic. To write the inverse of a conditional statement, you negate both the hypothesis and the conclusion of the original statement. In the case of the conditional statement you've provided, "If I live in Charleston, then I live in South Carolina," the hypothesis is living in Charleston, and the conclusion is living in South Carolina.
The inverse of your conditional statement would be "If I do not live in Charleston, then I do not live in South Carolina." Remember that creating the inverse of a conditional statement does not necessarily preserve the truth value of the original statement.
To demonstrate this, consider that the original statement is true because Charleston is indeed in South Carolina. However, the inverse might be false because not living in Charleston does not guarantee that one doesn't live in South Carolina - there are many other places within the state where one might reside.