Deductive Reasoning

Deductive reasoning is as simple as combining the pieces of a jigsaw puzzle to arrive at a conclusion. Numerous premises is collected and confirmed with each other, to arrive at a logical conclusion. In deductive reasoning, the probability of getting the final statement as true is very high since it is based on rules and logic. The conclusions derived from deductive reasoning can be highly dependable.

Let us learn more about deductive reasoning, types of deductive reasoning, the difference between deductive reasoning and inductive reasoning, with the help of examples, FAQs.

Deductive reasoning is a simple form of arriving at a conclusion by joining two or more pieces of information. It is a process of logical reasoning which processes two or more premises to arrive at a logical conclusion. Deductive reasoning does not depend on approximation or the concept of guessing. Deductive reasoning takes in a lot of premises or observations and confirms one premise with another premise to arrive at a conclusion. Deductive reasoning is often used to test the hypothesis and theorems.

Deductive reasoning is more dependable than inductive reasoning, which is based on assumption, whereas deductive reasoning is based on logical conclusions. Inductive reasoning cannot be fully relied upon, but deductive reasoning can be fully relied on as the conclusion is based on pure logic.

In deductive reasoning, the probability of getting the final statement as true is very high since it is based on rules and logic. If A = B, and B = C, then we can deduce it as A = C. Mathematical induction even though it has induction mentioned in it, is not inductive reasoning but is a form of deductive reasoning. The simplest form of deductive reasoning is syllogism, which has the first premise, and it is confirmed with the second premise to arrive at a conclusion.

Deductive reasoning helps confirm the validity of an argument. The conclusion of the deductive reasoning can be relied on, only if the premise is valid. Every student coming by bus scores A grade in his studies. Rahul goes by bus to school. Hence Rahul scores a A grade. This conclusion in this case is false because the premise is false.

Deductive reasoning can be solved across the following sequence of logical steps.

• A set of premises satisfying a particular logic are collected.
• The validity of the first premise is confirmed with another premise.
• The two premises are logically connected, and summarized to arrive at a conclusion statement.

The different types of deductive reasoning are based on the premises and the kind of relationship across the premises. The three different types of deductive reasoning are syllogism, modus ponens, and modus tollens. Let us check in detail about each of the deductive reasoning methods.

Syllogism

A syllogism is a common form of deductive reasoning which includes a set of premises followed by a concluding statement. The first premise is a conditional statement, and the second premise is another conditional statement which connects with the conclusion of the first premise. And the summary statement concludes by combining the first part of the first premise with the second part of the second premise.

• The numbers which are divisible by 2 are multiples of the number 2.
• The multiples of the number 2 are all even numbers.
• The numbers which are divisible by 2 are all even numbers.

Modus Ponens

This type of deductive reasoning can also be referred to as affirming the antecedent because the first statement is generally a conditional statement. And the second statement merely affirming the first part of the previous statement. Let us look at the below example to clearly understand this concept of modus ponens.

• If a number lies between 99 and 999 then it is a three digit number.
• The number N is a number lying between 299 and 399.
• Therefore the number N is a three-digit number.

Modus Tollens

Another important form of deductive reasoning is modus tollens, and it is also referred to as the law of contrapositive. This is also referred as the law of contrapositive, since it is opposite to that of modus ponens. Here the second statement contradicts the first part of the conditional statement.

• The numbers 4 and 5 are the factors of 20
• The number X is not a factor of 20
• Therefore X is neither 4 nor 5

The following between deductive reasoning and inductive reasoning is shows below in the following table.

☛ Related Topics

The following topics help in a better understanding of deductive reasoning.

• Linear Programming
• Types of Functions
• Data Handling
• Domain and Range

What Is Deductive Reasoning In Maths?

Deductive reasoning is a logical method of arriving at a conclusion based on logic. The information is collected as premise and one premise is confirmed with another premise, to arrive at a conclusion. The conclusion of a deductive reasoning is not based on probability and can be fully relied on, and is dependable.

How To Apply Deductive Reasoning?

Deductive reasoning can be applied in a sequence of steps. Two or more premise related to a particular aspect is collected. These premises are logically connected to make meaning. Finally, the premise is all summarized to arrive at a conclusion.

What Are The Types Of Deductive Reasoning?

The different types of deductive reasoning is based on how the premises are connected to arrive at a conclusion. The three important types of deductive reasoning statements are syllogism, modus ponens, modus tollens.

What Is The Difference Between Deductive Reasoning And Inductive Reasoning?

Deductive reasoning and inductive reasoning differ in the way the conclusions are deduced. Deductive reasoning is based on pure logic and inductive reasoning is based on approximation. Inductive reasoning takes a premise from a sample to arrive at a conclusion about the population. But deductive reasoning logically confirms and connects one statement with another statement to arrive at a conclusion.

What Are The Uses Of Deductive Reasoning?

The deductive reasoning have wide applications in forming business strategies, in science research, in creating policy framework. The most important use of deductive reasoning is in solving business problems.