Question

What is the difference between Inductive and Deductive Reasoning?

Answer 1

Mathematical reasoning is important as it helps to develop critical thinking and understand Maths in a more meaningful way. These are the 7 types of reasoning which are used to make a decision. But, in mathematics, the inductive and deductive reasoning are mostly used.

Complete step by step answer:

Inductive Reasoning	Deductive Reasoning
In the Inductive method of mathematical reasoning, the validity of the statement is checked by a certain set of rules and then it is generalized.	The principle of deductive reasoning is the opposite of the principle of induction.
The principle of mathematical induction uses the concept of inductive reasoning.	The principle of mathematical induction uses the concept of deductive reasoning (contrary to its name).
As inductive reasoning is generalized, it is not considered in geometrical proofs.	In deductive reasoning, we apply the rules of a general case to a given statement and make it true for particular statements.
Inductive reasoning is non-rigorous logical reasoning and statements are generalized.	Deductive reasoning is rigorous logical reasoning, and the statements are considered true if the assumptions entering the deduction are true.
Example of Inductive Reasoning:Statement: The cost of goods is Rs 10 and the cost of labour to manufacture the item is Rs. 5. The sales price of the item is Rs. 50.Reasoning: From the above statement, it can be said that the item will provide a good profit for the stores selling it.	Example of Deductive Reasoning:Statement: Pythagorean Theorem holds true for any right-angled triangle.Reasoning: If triangle XYZ is a right triangle, it will follow Pythagorean Theorem.

Note: We must note that in maths, deductive reasoning is considered to be more important than inductive. The concepts of reasoning not only help the students to have a deeper understanding of the subject but also helps in having a wider perspective to logical statements.