Write the​ converse, inverse, and contrapositive of the statement below. Determine the truth value of each statement. If a statement is​ false, give a counterexample.

Question

If i am in Florida, then i am in the south

Answer 1

Converse: If I am in the south, then I am in Florida.
Truth value: False. Counterexample: If I am in Texas, I am in the south but not in Florida.

Inverse: If I am not in Florida, then I am not in the south.
Truth value: False. Counterexample: If I am in Georgia, I am not in Florida but I am still in the south.

Contrapositive: If I am not in the south, then I am not in Florida.
Truth value: True. Since the contrapositive is logically equivalent to the original statement, it is true.

Answer 2

Question content area bottom
Part 1
Write the converse of the conditional. Choose the correct answer below.
A.
If I am not in the ​, then I am not in .
B.
If I am not in ​, then I am not in the .
C.
If I am in the ​, then I am in .
D.
If I am in the ​, then I am not in .
Part 2
Determine the truth value of the converse. Choose the correct answer below.
A.
The converse is false. I can be in and not be in the .
B.
The converse is false. I can be in and still be in the .
C.
The converse is true.
Part 3
Write the inverse of the conditional. Choose the correct answer below.
A.
If I am not in the ​, then I am not in .
B.
If I am in ​, then I am not in the .
C.
If I am in the ​, then I am in .
D.
If I am not in ​, then I am not in the .
Part 4
Determine the truth value of the inverse. Choose the correct answer below.
A.
The inverse is false. I can be in and not be in the .
B.
The inverse is true.
C.
The inverse is false. I can be in and still be in the .
Part 5
Write the contrapositive of the conditional. Choose the correct answer below.
A.
If I am not in the ​, then I am in .
B.
If I am not in the ​, then I am not in .
C.
If I am not in ​, then I am not in the .
D.
If I am in the ​, then I am in .
Part 6
Determine the truth value of the contrapositive. Choose the correct answer below.
A.
The contrapositive is false. I can be in and not be in the .
B.
The contrapositive is false. I can be in and still be in the .
C.
The contrapositive is true.

Answer 3

Part 1: The correct answer is D. If I am in the south, then I am not in Florida.
Part 2: The correct answer is B. The converse is false. I can be in the south and still not be in Florida.
Part 3: The correct answer is A. If I am not in Florida, then I am not in the south.
Part 4: The correct answer is B. The inverse is true.
Part 5: The correct answer is B. If I am not in the south, then I am not in Florida.
Part 6: The correct answer is C. The contrapositive is true.