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For how many values of n, will P(n) be false?

Mathematics Asked by Asad Ahmad on November 29, 2020

We know that $P(2018)$ is true, then surely $P(n)$ will be true for all $n>2018$.

For $n<2018$, we can say that $P(2018)$ can only be true, if $P(2017)$ is true, which in-turn is true only if $P(2016)$ is true and so on…

So $P(n)$ should be true for all $n$. Thus Option A should be correct.

But the given answer is Option C. Can anyone help me with this?

2 Answers

Nowhere does it say that the only way $P(n+1)$ can be true is when $P(n)$ is true. So there's no need for the statement to be true for 2017 and less

Answered by Kartik on November 29, 2020

"For n<2018, we can say that P(2018) can only be true, if P(2017) is true, which in-turn is true only if P(2016) is true and so on..."

Wrong. IF $P(n)$ is true then $P(n+1)$ is true, but if $P(n+1)$ is true, $P(n)$ can be either true or false. The correct statement would be: If $P(n+1)$ is false, then $P(n)$ is false too.

Answered by YJT on November 29, 2020

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