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Last Updated: Jun 30, 2023

Deductive reasoning- concepts and problems

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Introduction

Deductive reasoning is a process of drawing logically concrete conclusions from one or a few statements with the help of reasoning.

It needs us to use our problem-solving skills and reasoning skills to make logical conclusions and evaluate arguments.

The most important thing in deductive reasoning is that we need to rely on the information given solely and not on our knowledge. 

There are three common types of deductive reasoning-

  • Syllogisms- In this type of deductive reasoning, we have a few sentences used as premises/rules, and another statement serves as the conclusion. 

For example- (A)If a person is born in the 2010s, they are called kids.

(B)If a person is a kid, they must not use mobile. 

(C)Therefore, if a person is born in the 2010s, they must not use mobile.

  • Modus ponens- In this type of logical reasoning, we have a conditional statement, then an antecedent of the conditional statement. And the consequent of the conditional statement as the conclusion.

For example- (A)If a person is between 2010 and 2020, he is a kid.

(B)Ram was born in 2015.

(C)Ram is a kid.

  • Modus tollens- In this type of logical reasoning, we have a conditional statement and the negation of the consequent as a second statement. Then we have the negation of the antecedent as the conclusion.

For example- (A)If I am writing, then I am listening to music.

(B)I am not listening to music.

(C)Thus, I am not writing.

Types of problems

Problems on deductive reasoning can be divided into the following categories -

Problems on syllogisms

In this type of deductive reasoning, we have a few sentences used as premises/rules for the problem, and another statement serves as the conclusion. Then we have to check if the conclusion is valid or not. 

Problems with arrangements

It is another form of problem in deductive reasoning, in which we are given information about the order of arrangements of objects and based on that information. We need to draw conclusions about the order of objects or may be asked to tell the whole order of objects depending on the problem.

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Sample problems

Question-1 

A-All cricket players are fit and healthy.

B-All famous sportspeople are cricketers.

C-All famous sportspeople are fit and healthy.

If statements A, B are true, then tell if the C is true or not?

Answer- C is true.

Question-2 

A- In our seventh standard this year, 90% of students achieved 7 to 10 CGPA.

B- Last year, 92% of students achieved 7 to 10 CGPA.

C- The school thinks that the new approach had a brilliant impact on the performance of students.

If statements A, B are true, then tell if the C is true or not?

Answer- C is false.

Question-3 

A- Khali is stronger than John Cena

B- But John Cena is stronger than The Rock.

C- The Rock is stronger than Khali.

If statements A, B are true, then tell if the C is true or not?

Answer- C is false. 

Eight people are sitting around a dinner table facing inwards.

G is two seats to A’s left.

B is three seats to G’s right.

E is two seats to G’s left.

F is six seats to H’s right.

D is six seats to F’s right.

C is not sitting next to G.

Who sits one seat to D’s left?

(a) C

(b) F

(c) G

(d) H

Answer- (a) C.

Explanation- let’s see the representation of each step-

1-

 

2-

3-

4-

5-

Thus the person on one seat to D’s left is C.

Frequently Asked Questions

  1. What is deductive reasoning?
    It is a logical process in which we draw conclusions based on a few rules established by us.
     
  2. How to solve arrangement problems in deductive reasoning?
    To solve the arrangements problems based on deductive reasoning, you should start with representing each statement in a graphical form. Finally, you will have the arrangement of objects in the given order. Then you can answer the asked questions.
     
  3. What are syllogisms?
    It is a type of deductive reasoning in which we lay out a few rules or premises and then conclude based on them. 
     
  4. How is inductive reasoning different from deductive reasoning?
    Inductive reasoning is based on using observations to lay out rules or set up premises. In the case of deductive reasoning, we draw out specific conclusions based on the predefined rules/premises.
     
  5. What are the types of deductive reasoning?
    Based on the premises and conclusions, deductive reasoning is generally divided into three categories-
    Syllogisms
    Modus ponens
    Modus tollens

Key Takeaways

In this blog, we learned about deductive reasoning, which is an important topic for aptitude rounds of any exams. 

We started with learning about the types of deductive reasoning then the types of problems generally asked around it. Then we practiced the discussed concepts with the help of some examples.

You can learn more important topics for aptitude exams here and practice similar problems on Code studio.

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