Am I CORRECT .
Write the inverse and the contrapositive of the statement
If Jane is here, then she is well.
Inverse
To find the inverse of a conditional statement, you need to negate both the hypothesis and the conclusion of the original statement.
The original statement is: "If Jane is here, then she is well."
Negating the hypothesis ("Jane is here") gives us: "If Jane is not here..."
Negating the conclusion ("she is well") gives us: "...then she is not well."
So, the inverse of the statement "If Jane is here, then she is well" is: "If Jane is not here, then she is not well."
Now, let's move on to the contrapositive.
The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion and then reversing them.
Using the original statement:
- Negating the hypothesis ("Jane is here") gives us: "If Jane is not here..."
- Negating the conclusion ("she is well") gives us: "...then she is not well."
Finally, we reverse the order to get: "If she is not well, then Jane is not here."
So, the contrapositive of the statement "If Jane is here, then she is well" is: "If she is not well, then Jane is not here."