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Let no be any integer (positive, negative, or zero). Let Pno) Pno+1, tions, one for each integer n > no, such that .., Pn,..

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Answer #1

n_{0} be any positive integer and Pro Pt1.Py. be propositions .

Now given that no is true and P. implies Pn+1 .

From here using induction on n we can claim that P. is a true statement for all n no .

Proof : Suppose m is not true ,

Pm-1 is not true , because if m-1 true then m by given condition in (b) .

\Rightarrow  P_{m-2} is not true .

\Rightarrow P_{m-3} is not true .

.........

no is not true , a contradiction .

Hence \Rightarrow P_{n} is true for all n no .

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