Answer:
B.) If the ground is not wet, then it is not raining.
Explanation:
In logical terms, this can be written as [tex]P-- > Q[/tex], where:
- [tex]P[/tex] is "It is raining."
- [tex]Q[/tex] is "The ground is wet."
We need to find a statement that is logically equivalent to this.
Option A: If the ground is wet, then it is raining - INCORRECT
This statement is Q-->P. This is the converse of the original statement, and it is not logically equivalent.
Option B: If the ground is not wet, then it is not raining - CORRECT
This is the contrapositive of the original statement. In logic, a statement is always logically equivalent to its contrapositive.
Option C: It is not raining if the ground is wet - INCORRECT
This is neither the converse nor the contrapositive of the original statement and is not logically equivalent.
Option D: The ground is wet only if it is raining - INCORRECT
This is the converse. As noted earlier, the converse is not logically equivalent to the original statement.
Therefore, the correct answer is:
B.) If the ground is not wet, then it is not raining.