What is the difference between Inductive and Deductive Reasoning?
Answer
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Hint: 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:
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.
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.
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