If it is a holiday, then the office is closed. Today is not a holiday. Therefore

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Question: If it is a holiday, then the office is closed. Today is not a holiday. Therefore, the office is open. Is this conclusion valid?

Options:

Correct Answer: No

Solution:

The conclusion is not valid because the office could be closed for other reasons even if today is not a holiday.

If it is a holiday, then the office is closed. Today is not a holiday. Therefore, the office is open. Is this conclusion valid?

If it is a holiday, then the office is closed. Today is not a holiday. Therefore, the office is open. Is this conclusion valid?

Step 1: Understand the statement 'If it is a holiday, then the office is closed.' This means that holidays are a reason for the office to be closed.
Step 2: Note that today is not a holiday. This means the condition for the office being closed (it being a holiday) is not met.
Step 3: However, just because today is not a holiday does not mean the office must be open. The office could be closed for other reasons (like maintenance or a special event).
Step 4: Therefore, the conclusion 'the office is open' is not necessarily true, making it invalid.

Logical Implication – Understanding the relationship between premises and conclusions in logical statements.
Contrapositive Reasoning – Recognizing that the absence of a condition does not necessarily imply the absence of the outcome.