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  4. Statement I Any subset of R that is an inductive set must contain N. Statement II A set S is said to be an inductive set, if 1 ∈ S and x+1 ∈ S, whenever x ∈ S.

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Q. Statement I Any subset of $R$ that is an inductive set must contain $N$.
Statement II A set $S$ is said to be an inductive set, if $1 \in S$ and $x+1 \in S$, whenever $x \in S$.

Principle of Mathematical Induction

Solution:

We know, the set of natural numbers $N$ is a special ordered subset of the real numbers. Infact, $N$ is the smallest subset of $R$ with the following property.
A set $S$ is said to be an inductive set, if $1 \in S$ and $x+1 \in S$ whenever $x \in S$. Since, $N$ is the smallest subset of $R$ which is an inductive set, it follows that any subset of $R$ that is an inductive set must contain $N$.
So, both the statements are true and Statement II is the correct explanation of Statement I.