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

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 false

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
`P(n)=n^(2)-n+41`
`P(3)=47`
`P(5)=61`
Both are prime.
In fact the first composite number in the set of naturals is `P(41)=(41)^(2)`,
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