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

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?

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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