If Gina cleans her room, then she will go to the mall.
Which of these is logically equivalent to the given statement?
Answer
A. If Gina did not go to the mall, then she did not clean her room.
B. If Gina did not go to the mall, then she cleaned her room.
C. If Gina cleaned her room, then she will not go to the mall.
D. If Gina did not clean her room, then she will go to the mall.
I'll be glad to check your answer.
I agree.
To determine the logical equivalence of the given statement, let's break down the original statement: "If Gina cleans her room, then she will go to the mall."
The original statement follows the form "If P, then Q," where P represents "Gina cleans her room" and Q represents "she will go to the mall."
The logical opposite of "If P, then Q" is "If not P, then not Q."
Now let's examine each option:
A. "If Gina did not go to the mall, then she did not clean her room."
This option is not logically equivalent to the original statement because it states that if Gina did not go to the mall, then she did not clean her room. However, in the original statement, it is not implied that if Gina did not go to the mall, then she did not clean her room.
B. "If Gina did not go to the mall, then she cleaned her room."
Similarly to option A, this option is also not logically equivalent to the original statement because it states that if Gina did not go to the mall, then she cleaned her room. This is not implied in the original statement.
C. "If Gina cleaned her room, then she will not go to the mall."
This option is also not logically equivalent to the original statement. It swaps the conditions and claims that if Gina cleaned her room, then she will not go to the mall. This contradicts the original statement.
D. "If Gina did not clean her room, then she will go to the mall."
This option is the logical opposite of the original statement: it states that if Gina did not clean her room (not P), then she will go to the mall (not Q). Therefore, this option is logically equivalent to the given statement.
So, the answer is option D.