Question

Consider the statement: “P(n) : n² – n + 41 is prime." Then which one of the following is true?

Options

• Both P(3) and P(5) are true.

• P(3) is false but P(5) is true.

• Both P(3) and P(5) are false.

• P(5) is false but P(3) is true.

Answer 1

Both P(3) and P(5) are true.

Explanation:

P(n) = n² – n + 41

⇒ P(3) = 9 – 3 + 41 = 47 (prirne)

and P(5) = 25 – 5 + 41 = 61 (prime)

∴ P(3) and P(5) are both prime i.e., true.