State a modified form of the Second Principle of Induction s

State a modified form of the Second Principle of Induction similar to the modified form of the First Principle of Induction.

Solution

Solution:

Second principle of induction:

Let S be a subset of N such that,

i) 1 belongs to S and

ii) {1,2,3,..............,k} subset of S. i.e 1,2,...........,k belongs to S.

Then S=N. (N is the aet of all natural numbers).