A student argues: 'All prime numbers greater than 2 are odd. The number 15 is odd. Therefore 15 is prime.' What is wrong with this argument?
Answer and explanation
Correct answer: D. It reverses the implication: being odd does not make a number prime
- Step 1: The first statement says 'prime greater than 2 odd'. The argument uses the converse 'odd prime'.
- Step 2: Counterexample: is odd and not prime.
Answer
It reverses the implication: being odd does not make a number prime.
Why not the others: The argument is invalid ( is odd and not prime). Not all primes are even ( is the only even prime), is odd, and the first statement 'all primes greater than are odd' is true even though some odd numbers are not prime.
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