Deductive reasoning is defined as a logical process in which a conclusion is drawn based on the concordance of multiple premises that are generally assumed to be true. Deductive reasoning is also referred to as top-down logic. It is a logical approach where you progress from general ideas to specific conclusions through statements in mathematical reasoning.

A premise is a generally accepted fact, or rule, and it is a statement that lays the groundwork for a theory or general idea. Conclusions are statements which are supported by premises.

We first see the given premises then we derive a conclusion from both the premises which must be valid according to both the given premises. This process of finding a logical relation between the two premises is called Deductive Reasoning.

For example,

Premise 1: “All insects have six legs.”

Premise 2: “Spiders have eight legs.”

Using Deductive Logical Reasoning we can conclude the following.

Conclusion: “Spiders are not insects.”

We see that the above conclusion is valid with respect to both the provided premises.

Deductive reasoning is an important skill for individuals of all types, as it will allow one to make an inference based on two or more pieces of information.

## Types of Deductive Reasoning

There are mainly three types of deductive reasoning questions as listed below.

**Syllogism :**Syllogisms is a type of deductive reasoning which always appears in the three-line form, with a common term that appears in both the premises but not in the conclusion.

Given below is a deductive reasoning example for syllogism,

P: “If a person is born in the 1970s then they are in generation X.”

Q: “If a person is in Generation X then they have listened to music in a walkman.”

So the conclusion according to syllogism is “if a person is born in the 1970s then they have listened to music in a walkman.

**Modus Ponens :**This type of reasoning is also called “affirming the antecedent,” because only the first premise is a conditional statement whereas the second premise merely affirms to which the first part of the previous statement applies to be true..

Given below is a deductive reasoning example for Modus Ponens,

P: “If a person is born between 1981 and 1996 then they are a millennial.”

Q: “John was born in 1992.”

So the conclusion according to Modus Ponens is “John is a millennial.”

**Modus Tollens**: It is another type of deductive reasoning question, which is also called “the law of contrapositive.” It is the opposite of modus ponens because its second premise negates the second part of the previous statement.

Given below is a deductive reasoning example for Modus Tollens,

P: “If a person is born between 1981 and 1996 then they are a millennial.”

Q: “Brian is not a millennial.”

So the conclusion according to Modus Tollens is “Brian was not born between 1981 and 1996.”

## Steps to Solve Deductive Reasoning Questions

The steps to solve Deductive Reasoning Questions are listed below.

**Step 1: Make initial assumptions.**

We must begin by making an initial assumption that is generally accepted as true.

**Step 2: Form a second premise.**

Then consider a second the premise which is related to it. If the initial assumption is correct then the second premise is as well.

**Step 3: Conduct testing.**

We can then test the assumption in different scenarios and note the results.

**Step 4: Come to a conclusion.**

Depending on what results we obtain, we can then conclude whether the information is valid or invalid.

## Deductive Reasoning Vs Inductive Reasoning

The differences between Inductive and Deductive Reasoning is tabulated below.

Deductive Reasoning | Inductive Reasoning |

It is a logical process where a conclusion is based on the concordance of multiple premises that are generally assumed to be true. | It is a logical process where multiple premises that are assumed true are combined to obtain a specific conclusion. |

It varies from general to specific. | It varies from specific to general. |

It is a top down approach. | It is a bottom down approach. |

Its conclusion is true if the premises are true. | The conclusion may not be true although the premises may be true. |

It is based on facts, truth, or rules. | It is based on patterns or connections. |

It is more difficult to use as it is based on true facts. | It is used in daily life as it is based on evidence rather than facts. |

## Application of Deductive Reasoning

Deductive reasoning is a crucial skill that is valued in many different jobs and industries. It is widely applied in many different industries and valued by employers. The main applications of deductive reasoning are listed below.

- A marketing professional may use deductive logical reasoning to formulate and test advertising strategies.
- It is useful for people in management positions who have to make critical business decisions every day.
- It helps to test a hypothesis by implementing a solution that resolves the reason for the issue.
- In hiring a candidate the deductive reasoning test demonstrates a candidate’s ability to analyze and interpret information to make a logical deduction. This is generally more relevant for highly skilled roles, but also useful for almost every job application.
- Recruiters and employers use deductive reasoning tests as part of the application process before an interview as this type of test is easy to apply on a range of candidates, irrespective of their specific knowledge or skill set.

## Deductive Reasoning Solved Examples

**Problem 1:**X: “All footballers are healthy and fit.”Y: “All the famous sports players are footballers.”

Given that the above statements are true, find which of the following is the logical deduction.

- “All footballers are famous sports people.”
- “All famous people are healthy and fit.”
- “All famous sports players are healthy and fit.”
- “All fit and healthy people are footballers.”
- “All football players are men.”

**Solution:**

We first simplify the given facts.

- We cannot deduce that all footballers are famous sports people, as we do not have that information.
- We cannot deduce that all famous people are healthy and fit, because the fact is about famous sports people.
- This is the logical answer as we conclude that all famous sports players are healthy and fit.
- This information is also not given so all footballers are healthy and fit but we cannot logically link that all healthy and fit people are footballers.
- This is obviously incorrect as no gender is mentioned in the question.

Hence we get that number 3 is the correct logical deduction which is “All famous sports players are healthy and fit.”

**Problem 2:**In our Sixth Form this year, 94% of students achieved A to C grades. Last year, 95% of students achieved A to C grades. The school has said that its new approach to mentoring students has had a brilliant impact on student performance.

Based on the information above, which of the following statements are true?

- “Next year, student performance will be less than this year.”
- “All students taking A-Levels achieved A to C.”
- “Before last year, no students achieved A to C.”
- “Before last year, less than 94% of students achieved A to C.”
- “Every school has seen a rise in student performance.”

**Solution:**

With the given information, the only logical conclusion we derive is 4. Below we have described why other options are not logically correct.

- The student performance is increasing, so this cannot be correct given the facts.
- In this school 6% of students did not achieve A* to C.
- We do not have the data to make that deduction.
- We know that student performance has increased, so the year before last must have seen results below 94%.
- We do not have the information to deduce performance in other schools.

Thus the correct conclusion we deduce is “Before last year, less than 94% of students achieved A to C.”

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