How To Solve Syllogism Questions Quickly

February 28, 2020

Different Methods to solve Syllogism Questions

Solving Syllogism problems can be hard if you don’t know the correct way, in Syllogism we have a two Assumption Statements followed by Logical Conclusion and we have to tell which logical conculusion(s) is(are) true based on the Assumption Statements.

Let us try to understand what is Syllogism with an example –

Statements(Assumptions/Premises)

1. S1: All doctors are surgeons.

2. S2: Some chemists are doctors

Conclusions

1. Some chemists are surgeons.

2. All surgeons are chemists.

Statements need not make logical sense, we might have statements saying all pen are papers and all papers are erasers, which defies laws of nature, in such cases focus on the answer and forget logical laws.

How to solve Syllogism Question Quickly

There are three different methods to solve Syllogims which are –

Verbal Mehtod
Venn Diagram Method
Tick and Cross Method

Verbal Method –

It’s very simple one, try to make logical deductions in your mind from Assumptions (Premises) and match which conclusion is true.

Example –

Premises

All tigers are cats.
All cats are animals.

From these we can easily conlcude that since all tigers are necessarily cats and all Cats are necessarily animals. So, all tigers are animals.

Conclusion – All Tigers are Animals.

Venn Diagram Method –

There are four categories to remember to solve using Venn’s Diagram.

Rule 1 Syllogism

Statement – All A’s are B
Example – All Mangoes are Fruits

Conclusions that can be made out.

Conclusion 1 – Some A’s are B or Some Mangoes are Fruits
Conclusion 2 -Some B’s are A or Some Fruits are Mangoes.

Now, the first conclusion may confuse you as we said All A’s are B’s and then we are concluding some A’s are B’s.

In Syllogism its not wrong to say some A’s are B when you have a statement as All A’s are B’s, as –

Some A’s are actually B or Some Mangoes are actually fruit. This is not a wrong information

Rule 2 Syllogism

Statement – No A is B
Example – No Tomatoes are Fruits

This has a direct conclusion are No A is B

Rule 3 Syllogism

Statement – Some A’s are B
Example – Some men are Engineers

These have these possible conclusions –

Conclusion 1 – Some A are not B
Conclusion 2 – All A are B.
Conclusion 3 – All B are A
Conclusion 4 – All A are B and all B are A.

Now, Conclusion 1 is clear as if some men are Engineers then some may not be engineers (Check Image for Conclusion below Conclusion 2 two is a case when we for a sample set, only Engineers maybe allowed to do engineering. Similar of Conclusion 3 For Conclusion 4 both men and Engineers are same sample set i.e Sample Set(Men) = Sample Set(Engineers)

Rule 4 Syllogism

Statement – Some A’s are B
Example – Some animals are Tigers

These have two conclusions –

Conclusion 1 – Some A are B.
Conclusion 2 – No A is B.

Some handy How to Solve Syllogism Question Quickly & Rules –

All+All => All.
All+No => No.
All+Some => No Conclusion.
Some+All => Some.
Some+No => Some Not.
Some+Some => No Conclusion.

If the conclusion provided in the question is in “Possibility” case then you must proceed as per the following rules.

If All A are B => Some B are Not A is a Possibility.
If Some B are Not A => All A are B is a Possibility.
If Some A are B => All A are B is a Possibility & All B are A is a Possibility.

Summary for Venn Diagram

Now, in a few questions drawing diagrams may be very cumbersome as you may have to draw 4 diagrams depending upon the possibilities arriving specially Rule 3 which has 4 possibilities.

How to Solve Syllogism Questions Quickly

Ticks and cross solves the problem of not having to create many diagrams.

Ticks – They denote defined set
Cross – They denote undefined set

Defined Set – When all the elements of that set have to be known in order to define a particular premise.

Undefined Set – If all the elements of a set need not be known in order to make a particular statement

Each Syllogism Premise must be one of the four –

Universal Affirmative	All As are Bs.
Universal Negative	No As are Bs.
Particular Affirmative	Some As are Bs.
Particular Negative	Some As are not Bs.

Some Rules by Aristotle to solve Syllogism –

Checking if Conclusion is possible or not –

When Counting total premises and conclusion they should be 3
If we encounter a situation where in both the premises are negative then no conclusion can be achieved.
If we encounter a situation where in both the particular(some is used) are negative then no conclusion can be achieved.
The middle term (common term of both premises) must be distributed at least once.

Checking nature of conclusion –

If one premises is particular then conclusion will definitely be particular.
If one premises is negative then the conclusion will be negative.
A term that is not distributed in the premises cannot be distributed in the conclusion.

Learning with an Example –

Premises –

All parallelogram are four sided.
1. Some parallelograms are square.

Question 1.

Mentioned below are some statements followed by a conclusion in the options. Take the given statements to be true, even if they contradict to the commonly known facts, and determine the conclusions that logically follow the statements.

Statement:
1. All men are girls.
2. Some girls are students

Conclusion:
1. All girls are men
2. Some girls are not students.

Options:

A. The only Conclusion I follows

B. Only Conclusion II follows

C. Either conclusion I or Conclusion II follows

D. Neither conclusion I nor Conclusion II follows

Answer: D

Explanation:

Since both, the conclusions contain the term girls so neither of them can follow.

Hence option D is the correct one.

Question 2.

Statement:
1. All men are women.
2. All women are kids.

Conclusion:
1. All men are kids
2. Some men are not kids

Options:

A. The only Conclusion I follows

B. Only Conclusion II follows

C. Either conclusion I or Conclusion II follows

D. Neither conclusion I nor Conclusion II follows

Answer: A

Explanation:

By looking at the statements, it is evident that since all men are women and all women are kids, hence we can say that all men are kids. Thus it would be wrong to say that some men are not kids. Therefore the only conclusion I follow the statement.

Therefore one can say that option A is the correct one.

Question 3.

Statement:
1. All Roses are flowers.
2. No Orchid is Lotus

Conclusion:
1. No Orchid is a flower
2. Some Orchids are flowers.

Options:

A. The only Conclusion I follows

B. Only Conclusion II follows

C. Either conclusion I or Conclusion II follows

D. Neither conclusion I nor Conclusion II follows

Answer: C

Explanation:

Here, the first statement is a universal positive statement, so the middle term ‘Roses is forming the predicate is distributed twice. So the conclusion cannot be universal. Therefore, either conclusion I or II must be followed.

How To Solve Syllogism Questions: Venn Diagram method

Another easier way to solve syllogism questions is with the help of the Venn diagram.

All we have to do is, read the given statements and accordingly draw the Diagram step by step, by the given statements, and eventually derive a logical solution with the help of the final diagram.

It can be explained in a better way with the help of a couple of examples below:

Question 1.

Statement:
1. No oranges are Mangoes.
2. No mangoes are grapes.

Conclusion:
1. Some oranges are grapes
2. Some grapes are not mangoes.

Options:

A. The only Conclusion I follows

B. Only Conclusion II follows

C. Either conclusion I or Conclusion II follows

D. Neither conclusion I nor Conclusion II follows

Answer: D

Explanation

Here Since both the above statements are Negative, hence neither of the conclusion follows.

Therefore option D is the correct one.

Question 2.

Statement:
1. Some Jack is Jill
2. Some Max is Jack

Conclusion:
1. Some Jill is Max
2. No Jill is Max

Options:

A. The only Conclusion I follows

B. Only Conclusion II follows

C. Either conclusion I or Conclusion II follows

D. Neither conclusion I nor Conclusion II follows

Answer: C

Explanation:

By looking at the above diagram, it is evident that either conclusion I or conclusion II follow since the conclusion is forming a complementary pair.

Hence option C is the correct one.

Question 3.

Statement:
1. Some Tigers are Rats
2. No Hens are Tigers

Conclusion:
No Tigers are Hens
Some Rats are Hens

Options:

A. The only Conclusion I follows

B. Only Conclusion II follows

C. Either conclusion I or Conclusion II follows

D. Neither conclusion I nor Conclusion II follows

Answer: D

Explanation:

Since the first conclusion contains the middle term ‘puppy’ as the subject and the second conclusion contains the middle terms ‘puppy’ as the predicate. Since the conclusion I am particular, and conclusion II is negative. So, no conclusion follows.

Read Also – Formulas to solve syllogism questions

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3 comments on “How To Solve Syllogism Questions Quickly”

Chandra
Statement:
1. Some Tigers are Rats
2. No Hens are Tigers

Conclusion:
No Tigers are Hens
Some Rats are Hens

Options:

A. The only Conclusion I follows

B. Only Conclusion II follows

C. Either conclusion I or Conclusion II follows

D. Neither conclusion I nor Conclusion II follows

Answer: D
Explanation:

Since the first conclusion contains the middle term ‘puppy’ as the subject and the second conclusion contains the middle terms ‘puppy’ as the predicate. Since the conclusion I am particular, and conclusion II is negative. So, no conclusion follows.
//nowhere is written about puppy and you are justifying the conclusion based upon puppy how?

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Chandra
nothing mentioned about rat and hen.. how u have drawn the venn diagram between them?

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Chandra
Statement:
1. All men are girls.
2. Some girls are students

Conclusion:
1. All girls are men
2. Some girls are not students.

Options:

A. The only Conclusion I follows

B. Only Conclusion II follows

C. Either conclusion I or Conclusion II follows

D. Neither conclusion I nor Conclusion II follows

the answer should be both the conclusion 1 and 2 follows

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