Which of the following statements is logically equivalent to 'If it is raining,

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Question: Which of the following statements is logically equivalent to \'If it is raining, then the ground is wet\'?

Options:

Correct Answer: If the ground is not wet, then it is not raining.

Solution:

The contrapositive of the original statement is logically equivalent.

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

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

Step 1: Understand the original statement: 'If it is raining, then the ground is wet.' This is a conditional statement.
Step 2: Identify the parts of the statement: 'It is raining' is the hypothesis (P) and 'The ground is wet' is the conclusion (Q).
Step 3: Write the contrapositive of the statement. The contrapositive is formed by negating both parts and switching them: 'If the ground is not wet, then it is not raining.'
Step 4: Recognize that the contrapositive is logically equivalent to the original statement. This means both statements are true or false in the same situations.

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