Prove or disprove Recall Can use Direct Proofs Contrapositiv

Prove or disprove (Recall: Can use Direct Proofs, Contrapositive, Contradiction and/or Induction to prove statements, Counterezamples to disprove statements.)

Solution

Solution:

Recall the definition of prime number.

A natural number p greater than 1 is said to be prime, if it has no positive divisors other than 1 and itself.

We prove by contrapositive way: that if x is not odd then it is not prime. That is, it has a positive divisor other than 1 and x. Which will imply that if x is prime,then x is odd.

If x is not odd,then x is even. Let x =2k for some natural number k. clearly x has a factor 2 which is positive and not equal to 1 and x. Implies x is not prime.

Contrapositively, if x is prime then x is odd.