First Principle of Mathematical Induction

Elaborate the differences between Deductive and Inductive Reasoning?

What is deductive reasoning? State with examples.

State whether the following statement is true or false.

There are no positive integers strictly between $0 \& 1$. 

State whether the following statement is true or false.

The well-ordering principle is a property of the positive integers which is equivalent to the statement of the principle of mathematical induction.

Generalisation step is proved using

Which step concludes or proves the given statement 

A statement $P\left(n\right)$ is true, where $n$ is a natural number.

The assumption in the inductive step is called as inductive hypothesis is

A statement $P\left(n\right)$ is true, where $n$ is a natural number. Then

Consider a statement $P\left(n\right)$, where $n$ is a positive integers. Then in the verification step

Consider a statement $P\left(n\right)$, where $n$ is a natural number. Then in the verification step

$\frac{1}{n+1}+\frac{1}{n+2}+.\dots ..+\frac{1}{2n}>\frac{13}{24}$ is true for all $$

For every natural number $n, P\left(n\right)=n\left(n+1\right)$ is always

Identify the incorrect statement

Which of the following is not true?

Every even number is divisible by two. $1986$ is an even number. It is divisible by two.

Identify the reasoning process.

Jim has $20$ pencils. He gives half of them to Dan. Jim has $10$ pencils left.

James Cameron’s last three movies were successful. His next movie will be successful.

Identify the reasoning process.

I got up at nine o’clock for the past week. I will get up at nine o’clock tomorrow.

For every natural number $k$, which of the following is true?

Using principle of mathematical induction that, prove that $a^{2n}-b^{2n}$ is divisible by $a+b$.