Consider the statement: 'If an animal is a falcon, then it has feathers.' Which of the following is logically equivalent to this conditional statement?

Answer and explanation

Correct answer: A. If an animal does not have feathers, then it is not a falcon.

  1. Step 1: Recall formal logic equivalence: A conditional statement (P -> Q) is logically equivalent strictly to its contrapositive (~Q -> ~P).
  2. Step 2: Identify P and Q: P = 'animal is a falcon'; Q = 'animal has feathers'.
  3. Step 3: Form the contrapositive ~Q -> ~P: 'If an animal does not have feathers, then it is not a falcon.'
  4. Step 4: Conclude this is the only logically valid equivalent statement.
Answer
If an animal does not have feathers, then it is not a falcon.
Why not the others: 'If an animal has feathers, then it is a falcon' is the converse (Q -> P), which is a formal fallacy; 'If an animal is not a falcon, then it does not have feathers' is the inverse (~P -> ~Q), also invalid; 'All animals with feathers are falcons' restates the invalid converse universally.

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