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Question:

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

Both P(3) and P(5) are false

P(3) is false but P(5) is true

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

P(5) is false but P(3) is true

Solution:

P(n): n² - n + 41 is prime
P(5) = 5² - 5 + 41 = 25 - 5 + 41 = 61 which is prime
P(3) = 3² - 3 + 41 = 9 - 3 + 41 = 47 which is also prime.