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If it rains, the ground gets wet. The ground is not wet. Can we conclude that it

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Question: If it rains, the ground gets wet. The ground is not wet. Can we conclude that it did not rain?

Options:

  1. Yes
  2. No
  3. Only if it is not a water source
  4. Cannot be determined

Correct Answer: Yes

Solution: 

The conclusion is valid because if the ground is not wet, it logically follows that it did not rain.

If it rains, the ground gets wet. The ground is not wet. Can we conclude that it

Practice Questions

Q1
If it rains, the ground gets wet. The ground is not wet. Can we conclude that it did not rain?
  1. Yes
  2. No
  3. Only if it is not a water source
  4. Cannot be determined

Questions & Step-by-Step Solutions

If it rains, the ground gets wet. The ground is not wet. Can we conclude that it did not rain?
  • Step 1: Understand the statement 'If it rains, the ground gets wet.' This means that rain is the cause of the ground getting wet.
  • Step 2: Recognize that the opposite of the first statement is 'If the ground is not wet, then it did not rain.' This is a logical conclusion.
  • Step 3: Note that the ground is not wet. This is given information.
  • Step 4: Since the ground is not wet, we can use the logical conclusion from Step 2 to say that it did not rain.
  • Logical Implication – Understanding the relationship between conditions, specifically the contrapositive in logic.
  • Contrapositive Reasoning – Recognizing that if 'If A then B' is true, then 'If not B then not A' is also true.
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