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Let P(n) be a statement and let P(n) Rig...

Let P(n) be a statement and let P(n) `Rightarrow` P(n+1) for all natural number n, then P(n) is true.

A

For all `n in N`

B

For all `n ge m`, m being a fixed positive integer

C

For all `n ge 1`

D

Nothing canbe said.

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • Let P(n) be a statement such that P(n) Rightarrow P(n+1) for all n in NN . Also, if P(k) is true, k in N , then we can conclude that.-

    A
    P(n) is true for all n
    B
    P(n) is true for all n `n ge k`
    C
    P(n) is true for all n `n gt k`
    D
    None of these

  • Let P(n) be a statement such that truth of P(n)implies the truth of P(n + 1)[ n in N, then P(n) is true

    A
    `AA n gt 1`
    B
    `AA n`
    C
    Nothing can be said
    D
    `AA n gt k` ( k is some fixed positive integer )

  • Let P(n): n^(2)+n is odd, then P(n) Rightarrow P(n+1) for all n. and P(1) is not true. From here, we can conclude that

    A
    P(n) is true for all `n ge NN`
    B
    P(n) is true for all `n ge 2`
    C
    P(n) is false for all `n in NN`
    D
    P(n) is true for all `n ge 3`