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In a logical argument, if 'P implies Q' is true, which of the following is a val

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Question: In a logical argument, if \'P implies Q\' is true, which of the following is a valid conclusion?

Options:

  1. If Q is true, then P must be true.
  2. If P is false, then Q must be false.
  3. If P is true, then Q must be true.
  4. If Q is false, then P must be false.

Correct Answer: If P is true, then Q must be true.

Solution: 

In logic, if \'P implies Q\' is true, it means that whenever P is true, Q must also be true.

In a logical argument, if 'P implies Q' is true, which of the following is a val

Practice Questions

Q1
In a logical argument, if 'P implies Q' is true, which of the following is a valid conclusion?
  1. If Q is true, then P must be true.
  2. If P is false, then Q must be false.
  3. If P is true, then Q must be true.
  4. If Q is false, then P must be false.

Questions & Step-by-Step Solutions

In a logical argument, if 'P implies Q' is true, which of the following is a valid conclusion?
  • Step 1: Understand what 'P implies Q' means. It means if P is true, then Q must also be true.
  • Step 2: Recognize that 'P implies Q' does not say anything about what happens if P is false. Q can be true or false in that case.
  • Step 3: Identify that a valid conclusion from 'P implies Q' is that if P is true, then Q is true.
  • Step 4: Remember that you cannot conclude that P is true just because Q is true, as Q could be true for other reasons.
  • Implication in Logic – 'P implies Q' means that if P is true, then Q must also be true. It does not state anything about the truth of P or Q independently.
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