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Which of the following statements is logically equivalent to “If it is raining, then the ground is wet”?

A) If the ground is wet, then it is raining.
B) If the ground is not wet, then it is not raining.
C) It is not raining if the ground is wet.
D) The ground is wet only if it is raining.

Sagot :

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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.

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