Logical Deductions | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

Logical deduction is a process of reasoning where one derives a logically necessary conclusion from given premises. In other words, it involves drawing conclusions based on a set of statements or conditions that are provided. Logical deduction is a crucial skill in various competitive exams, including the Common Admission Test (CAT) for management education.

What is Logical Deduction?

• Logical deduction is the process of drawing conclusions based on premises or statements that are known or assumed to be true. It involves using reasoning and logical principles to derive new information or insights.
• The main purpose of logical deduction is to make valid and sound arguments and arrive at accurate conclusions. It helps us analyze and evaluate information, solve problems, and make informed decisions.

How does Logical Deduction Work?

• Logical deduction operates on the principles of deductive logic. It starts with a set of premises or statements and applies logical rules to derive a conclusion. 
• This process ensures that the conclusion is necessarily true if the premises are true.

Logical Deductions Premises - Various Patterns

Type 1: If A Happens B Happens

• This means that A leads to B, but does not mean the reverse, i.e., if B has happened, A must have happened. In such situations, A is a sufficient condition for B, but is not a necessary condition.
• Let’s look at the following example:
  If I go to a movie, I enjoy myself.
  ~ This would mean, that if I have gone to the movie, I will definitely enjoy myself. However, it does not mean that if I have enjoyed myself, I must have gone to the movie—there are so many ways of enjoying yourself.
  Another example of this type would be:
  If Amir acts in a movie, he will earn money.
  ~This does not mean that if he has earned money, he must have acted in a movie.

Type 2: Only If A Happens B Happens

• In this case, A is a necessary and sufficient condition for the occurrence of B. In this case, there is reversibility of the logic, i.e., if B has happened, A must have happened.
• Example:
  Only if Saurav plays the match, will he get a hundred.
  ~ If Saurav has got a hundred, he must have played the match.

Type 3: If A Happens B Does Not Happen

• In this case, if A has happened, B does not happen. The opposite is also true, i.e., if B has happened, A must not have happened.
• Example:
  If Martina plays well, Sania will not win.

Type 4: If A does not Happen B will Happen

• Again in this case, the reverse might not be true.
• Example:
  If Anand does not come, Kasparov will. This does not mean that if Kasparov comes, Anand will not come.

Type 5: Either A or B will Happen

• One of the two has to happen. At the same time, the two events are exclusive of one another. If one happens, the other will not happen.
• Example:
  Either he becomes a TV star or he becomes a movie star.

Solved Examples

Example 1: Shahrukh either acts as a villain, or he acts as a hero.
A. Shahrukh acts like a hero.
B. Shahrukh does not act like a villain.
C. Shahrukh acts like a villain.
D. Shahrukh does not act like a hero.
(a) Only CD
(b) Only BA
(c) CD and BA
(d) None of these

This question is based on an EITHER-OR Premise. Thus, we can see that CD is correct. Since, if he acts like a villain—(Statement C) he will not act like a hero (Statement D). Similarly, BA can also be seen to be true. Hence option (c) is correct.

This question falls under the category of if A happens, then B does not happen. However, if B has not happened, it does not mean that A has happened.
AB and CD are both logically correct.

Example 3: You can find Chinese toys only in China.

A. I didn't find Chinese toys.
B. I found Chinese toys.
C. I went to the fair.
D. I didn't go to China. 

(a) CD
(b) CB
(c) CA
(d) DA

Ans: (d) 

Example 4: Either the bus is late, or it has turned turtle.

A. The bus is late.
B. The bus is not late.
C. The bus has turned turtle.
D. The bus has not turned turtle.

(a) AB
(b) DB
(c) CA
(d) BC

Ans: (d) 

Example 5: You cannot clear the CAT unless you are intelligent.

A. You are intelligent.
B. You can clear the CAT.
C. You are not intelligent.
D. You cannot clear the CAT.

(a) BD
(b) AC
(c) CD
(d) AB

Ans: (c)