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Consider the statement: "P(n): n^(2)-n+4...

Consider the statement: `"P(n): n^(2)-n+41` is prime". Then which one of the following is true?

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Given statement is "`P(n):n^(2)-n+41` is prime".
Clearly `(P(3):3^(2)-3+41=9-3+41`
`=47` which is a prime number.
and `P(5):5^(2) -5+41=25-5+41=61,`
which is also a prime number.
` therefore ` Both P(3) and P(5) are true.
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