# Definition of Various Terms

## Types of Reasoning in Maths

In terms of mathematics, reasoning can be of two major types which are:

1. Inductive Reasoning
2. Deductive Reasoning

Among the other types of reasoning are intuition, counterfactual thinking, critical thinking, backwards induction and abductive induction. 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 which are discussed below.

Note: Inductive reasoning is non-rigorous logical reasoning and statements are generalized. On the other hand, deductive reasoning is rigorous logical reasoning and the statements are considered true if the assumptions entering the deduction are true. So, in maths, deductive reasoning is considered to be more important than inductive.

### Inductive 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. As inductice reasoning is generalized, it is not considered in geometrical proofs. Here, is an example which will help to understand the inductive reasoning in maths better.

• Example of Inductive Reasoning:

Statement: The cost of goods is Rs 10 and the cost of labor 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.

### Deductive Reasoning

The principal of deductive reasoning is actually the opposite of the principle of induction. On the contrary to inductive reasoning, in deductive reasoning, we apply the rules of a general case to a given statement and make it true for particular statements. The principle of mathematical induction uses the concept of deductive reasoning (contrary to its name).The below-given example will help to understand the concept of deductive reasoning in maths better.

• 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.