Q67 / 170 · Manipal (MET) 2017 · Mathematics

If $P(n)$ is a statement such that $P(3)$ is true. Assuming $P(k)$ is true $\Rightarrow P(k+1)$ is true for all $k \geq 3$, then $P(n)$ is true

  • A
    for all $n$
  • Correct answer
    B
    for $n \geq 3$
  • C
    for $n \geq 4$
  • D
    None of these

Solution

Since, $P(3)$ is true. Assume $P(k)$ is true $\Rightarrow P(k+1)$ is true means, if $P(3)$ is true $\Rightarrow P(4)$ is true $\Rightarrow P(5)$ is true and so on. So, statement is true for all $n \geq 3$.

Hence, the correct answer is option: 'B'.

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