SYLLOGISM - LOGICAL DEDUCTION MADE EASY!

Hello Everybody!!

Engineering made me a bit busy. I couldn't post new stuff in my blog for a long time. Now I'm back and I have something new.

Syllogism or Logical Deduction is an interesting topic found in many analytical reasoning aptitude question papers. But for beginners, it would be confusing. This post would teach you each and every thing in syllogism. Step by step method to get an answer.Once you go through them, you'll be able to answer any any question in syllogism or logical deduction. In my next post, I'll provide a summary of rules, which helps to find the answer in a fraction of second.

Now let's start with syllogism.

Now Look at this question.

There are two statements below!
All youngsters are students.
All students are brilliant.

You can infer the following from the above statements.

1. There are three terms in totally in the two statements. They are 'youngster', 'student' & 'brilliant'.

2. The term 'student' is common in  both the statements.

Did you notice them??
Yes? Then it means you are familiar with the first rule.

RULE 1: There should be three terms in both the statements, with one term common in both of them.

When you find a question, which doesn't follow this rule, simply choose the option, 'No conclusions can be drawn.'

Look at this sample.

All sheets are papers.
All books are notes.

Conclusions: Some sheets are notes. Some books are papers.

There are four terms in the two statements and nothing is common. So just the answer is ' Both the conclusions are false.'

The first rule is the like 'qualifier'. The first rule would tell you whether any conclusions can be drawn are not. That is, it checks if the question has an answer or not. If yes, then rule 2 will help you to find out it.

RULE 2:

The first rule dealt with the distribution of terms. We didn't care about the word 'All' in the question.
Rule 2 deals with it.

Look at the following list of statements.

All boys are men.
Some boys are men.
Some boys are not men.
No boys are men.

Any statement you encounter, will be surely one of those four types.
That is, any statement would either have 'All' ,or 'Some' or 'Some not' or 'No'. I call them 'Keywords'.
Some times synonyms of these words are used.

Synonyms for all = Any, Each, Every.
Synonyms fir some = At least, Few, Many, Most of.

But what you see in questions is not a single statement, but a combination of two statements.
Both the statements in the question will be from those four types in any combination.

Now we shall extend the rule 2 to some sub-rules.

RULE 2A:

The statement Some A is B is same as Some B is A.

Hence, "Some boys are men" can be written as "Some men are boys."

RULE 2B:

The statement No A is B is same as No B is A.

Hence, "No boys are men" can be written as "No men are boys."

RULE 2C:

The statement No A is B can bed inferred as  Some A are not B and  Some B are not A.

Hence, "No boys are men" can be written as "Some boys are not men" can be written as "Some men are not boys."

RULE 2D:

This rule is very important.
The statement All A are B can be inferred as Some A are B and Some B are A.

Hence, "All boys are men" can be written as "Some boys are men." and "Some men are boys."

Never forget any of the above rules.
Now let's solve different possible types of problems.

TYPE 1:

ALL + ALL COMBINATION DIAGONAL:

Look at this question.

All mobiles are computers.
All computers are laptops.

Step 1: Look for keywords.
Statement 1 has 'All' & statement 2 also has 'All'.

Step 2: Now look at the terms. Find which term is common.
The term 'computer' is common.

Step 3: Now look the term computer's position. Whether they are straight or diagonal.
It is diagonal. (because, in 1st statement, computer is the 2nd term, & in 2nd statement, computer is the 1st term.)

The following observation can be denoted as
All x All

The solution for this type is

All x All  =  All

So the conclusions that we can derive the following conclusions.

All mobiles are laptops.
And of course by rule 2D, we also get,
Some mobiles are laptops.
Some laptops are mobiles.

TYPE 2:

ALL + ALL COMBINATION LINEAR.

Look at this question.

All computers are laptops.
All computers are mobiles.
Step 1: Look for keywords.
Statement 1 has 'All' & statement 2 also has 'All'.

Step 2: Now look at the terms. Find which term is common.
The term 'computer' is common.

Step 3: Now look the term computer's position. Whether they are straight or diagonal.
It is straight (linear). (because, in 1st statement, computer is the 1st term, & in 2nd statement, computer is the 2nd term.)

The following observation can be denoted as
All + All

The solution for this type is

All + All  =  Some

So the conclusions that we can derive the following conclusions.

Some laptops are mobiles.
And by rule 2A, we also get,
Some mobiles are laptops.

TYPE 3:

ALL + SOME COMBINATION.

Look at this question.

All computers are laptops.
Some computers are mobiles.
Step 1: Look for keywords.
Statement 1 has 'All' & statement 2 has 'some'.

Step 2: Now look at the terms. Find which term is common.
The term 'computer' is common.

Step 3: No need to check linearity when 'Some' is present in any one of the statement.
This is because of rule 2A. By this rule, Some A is B is same as Some B is A. So, the position doesn't matter when 'some' appears in any of the statements.

The following observation can be denoted as
All + Some
The solution for this type is

All + Some =  Some

So the conclusions that we can derive the following conclusions.

Some laptops are mobiles.
And by rule 2A, we also get,
Some mobiles are laptops.


TYPE 4:

ALL + SOME NOT COMBINATION.

Look at this question.

All computers are laptops.
Some computers are not mobiles.

Step 1: Look for keywords.
Statement 1 has 'All' & statement 2 also has 'some not'.

Step 2: Now look at the terms. Find which term is common.
The term 'computer' is common.

Step 3: Not needed because of Rule 2C.

The following observation can be denoted as
All + Some not

The solution for this type is

All + Some not  =  Some not

So the conclusions that we can derive the following conclusions.

Some laptops are not mobiles.

TYPE 5:

ALL + NO COMBINATION LINEAR.

Look at this question.

All computers are laptops.
No computers are mobiles.

Step 1: Look for keywords.
Statement 1 has 'All' & statement 2 also has 'No'.

Step 2: Now look at the terms. Find which term is common.
The term 'computer' is common.

Step 3: There is no some or some not used in any of the statements. Hence Checking linearity is needed. Now look the term computer's position. Whether they are straight or diagonal.
It is straight (linear). (because, in 1st statement, computer is the 1st term, & in 2nd statement, computer is the 1st term.)

The following observation can be denoted as
All + No

The solution for this type is

All + No  =  Some Not

So the conclusions that we can derive the following conclusions.
Some laptops are not mobiles.

TYPE 6:

ALL + NO COMBINATION Diagonal.

Look at this question.

All computers are laptops.
No laptops are mobiles.

Step 1: Look for keywords.
Statement 1 has 'All' & statement 2 also has 'No'.

Step 2: Now look at the terms. Find which term is common.
The term 'laptop' is common.

Step 3: There is no some or some not used in any of the statements. Hence Checking linearity is needed. Now look the term laptop's position. Whether they are straight or diagonal.
It is diagonal. (because, in 1st statement, laptop is the 2nd term, & in 2nd statement, laptop is the 1st term.)

The following observation can be denoted as
All x No

The solution for this type is

All x No  =  No

So the conclusions that we can derive the following conclusions.
No computers are mobiles
And by rule 2B and 2C, we also get,
Some computers are not mobiles.
Some mobiles are not computers.

TYPE 7:

This is the last type.
SOME + NO COMBINATION.

Look at this question.

Some computers are laptops.
No laptops are mobiles.

Step 1: Look for keywords.
Statement 1 has 'Some' & statement 2 also has 'No'.

Step 2: Now look at the terms. Find which term is common.
The term 'laptop' is common.

Step 3: The term some is found. Hence, by rule 2A, we can skip this step.

The following observation can be denoted as
Some + No
The solution for this type is

Some + No = Some not
So the conclusions that we can derive the following conclusions.
Some computers are not mobiles.

Now you may ask what happened for the following combinations.
No + No
Some + Some
Some + Some Not,
Some Not  +Some Not,
Some not + No

All these five give no conclusions.

Look at all of them, none of them has 'All' in it. None of them give particular information about the terms present in the statements.

Whenever you find such combinations, go for, ' No conclusions can be drawn.'

That's all guys.

Now you are an expert in Syllogism. My next post will have a summary of the above rules and types with problems for practice along with solution.

Hope it was useful.