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if P(n) be the statement 10n+3 is a prim...

if `P(n)` be the statement `10n+3` is a prime number", then prove that P(1) and P(2) are true but P(3) is false.

A

`n gt 2`

B

`n gt 3`

C

`n lt 4`

D

`n ge 2`

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • If P_(n) is the set of first n prime numbers, then underset(n=3)overset(10)capP_(n) is

    A
    {3,5,7,11,13,17,19}
    B
    {2,3,5}
    C
    {2,3,5,7,11,13,17}
    D
    {3,5,7}

  • If p_(n) is the set of first n prime numbers, then underset(n=2)overset(10)(U)P_(n)=

    A
    {2,3,5,7,11,13,17,19}
    B
    {3,5}
    C
    {2,3,5,7,11,13,17,19,23,29}
    D
    {2,3}

  • Let P(n) be the statement n^2 -n - 41 is prime , then which of the following is not true ?

    A
    `P(2)`
    B
    `P(3)`
    C
    `P(41)`
    D
    None of these

    • Similar Questions

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    If P(n) is the statement n^(2)-n+41 is prime. Prove that P(1),P(2) and P(3) are true. Prove also that P(41) is not true.

    If P(n) is the statement n(n+1)(n+2) is divisible is 12 prove that the statements P(3) and P(4) are true,but that P(5) is not true.

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    If P(n) is the statement n^(3)+n is divisible by 3, prove that P(3) is true but P(4) is not true.

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