Question

Proving "A prime number greater than 2 is odd." is an example of which type of proof?

• A. Direct proof
• B. Indirect proof

Answer 1

The correct option is B Indirect proof

Let p be the prime number.We have to prove p is odd if it is greater than 2.
Let us start the proof by assuming p is not odd.
So p is an even number
$\therefore$ a divisor of p is 2 ..... (I)
But it is given that p is a prime number greater than 2 ....(given)
$\therefore$ 1 and p are the only divisors of p ..... (II)
Statements (I) and (II) are contradictory.
$\therefore$ the assumption , that p is not odd is false.
This proves that a prime number greater than 2 is odd in indirect way of proof.