Syllogism Questions for DU JAT

The word Syllogism is derived from the Greek word ‘Syllogismos’ which means ‘Conclusion’. A Syllogism is a kind of logical justification that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.

The questions which are asked in the syllogism topic of logical reasoning section contain two or more statements, and two or more conclusions followed by the statements. You have to find out which conclusions are logically suitable according to the given statements. The statements have to be taken true even if they seem to be at variance from the commonly known facts.

The main and the most successful and logical way to solve Syllogism questions are by using Venn Diagrams. Considering the statements, you need to draw all the possible diagrams and solve each of them separately. Finally, the answer common to all the diagrams is taken as the correct one.

Syllogism is an important topic of logical reasoning. Generally, a set of 5 – 6 questions are asked in the Delhi University Joint Admission Test (DU JAT). These types of questions are to be solved using Venn Diagrams.

In this article, you will get all the types of Syllogism Questions for the Delhi University Joint Admission Test (DU JAT).

Types of Syllogism Questions

There are countless types of possible cases of syllogism questions, but below we have discussed the general types which are most likely to be asked in the DU JAT Exam.

1. All A are B

This case means that A is contained in B but not necessarily vice versa. This means A is a subset of B, but B may not be a subset of A. The Venn diagram for this is:

In the above Venn diagram, it is visible that circle A is inside circle B, which means that B contains the entire A, i.e. All A are B.

Example:

Statement: All Papers are magazines

All Papers are Books

Conclusion: All Books are Magazines

All Magazines are books

Some Papers are Magazines

Some Books are Paper

Some Magazines are Book

Solution:

In the below Venn diagram, you can see that All Papers are Magazines, and All Papers are Books

 Now, you look at all the conclusions and choose which is true. And which are false.

After looking at the conclusion we state that only (iii), (iv), (v) conclusion follows.

DU JAT mock test

DU JAT mock test

2. A = B

This case means that A is a subset of B and B is also a subset of A. The conclusion of this case is similar to the first type, i.e. “All A are B”. Here not only “All A are B”, but also “All B are A”.

3. No A are B

This case means that B does not contain any of A and so A is not contained in B. This means that A and B are disjoint sets. The Venn diagram for this case is:

Here no part of A is present inside of B and similarly, no part of A is present in A. So neither A nor B contain any part of B or A respectively.

Example:

Statement: No Black is Beauty

No Beauty in White

Conclusion: Some Blacks are not Beauty

Some Beauties are not White

Some Whites are not Black

Some Beauties are not Black

Some Blacks are not White

Solution:

In the below Venn diagram you can see that No Black is Beauty, No Beauty is White, and there is no relation between Black and White.

Now, you look at all the conclusion and choose which is true and which are false

After looking at the conclusion we state that only (ii), (i), (iv) conclusion follows.

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4. Some A are B

This case means when some of A is in B that is A and B are overlapping each other, and thus some B is A will also be true. The Venn diagram depiction is as:

Here, the slightly dark portion between A and B indicates that some portion of A is contained in B while the light blue portion is uncertain and does not indicate anything whether A is contained in B or not.

Example:

Statement:  Some A are B; Some B are C; Some C are D

Conclusion: No A are C; Some D are C; Some B are not A; No B are D; All C are D

Solution:

In the below Venn diagram you can see that Some A are B, Some B are C, and Some C are D and there is no relation between A and C, B and D, and A and D.

Now, you look at all the conclusions and choose which is true and which are false

After looking at the conclusion we state that only (ii) conclusion follows.

5. Some A are not B

This case means that some portion of A is not included in B for sure while the other part of A is uncertain whether it is included in B or not. The Venn diagram is;

In this, some portion of A is surely not included in B while there is no surety whether the slightly dark blue region is included in B or not

These are certain universal rules that should be followed while solving the syllogism questions. They are:

  1. Any “All” and “All” sentences will always imply an “All” conclusion.
  2. Any “All’ and “No” sentences will always imply a “No” conclusion.
  3. Any ``All” and “Some” sentences will always imply a “No” conclusion.
  4. Any “Some” and “All” sentences will always imply a “Some” conclusion.
  5. Any “Some” and “No” sentences will always imply a “Some not’ conclusion.
  6. Any “Some” and “Some” sentences will always imply a “No” conclusion.

Complementary Pairs

If the one conclusion is true (valid) and one conclusion is false (invalid) or vice – versa. Therefore, these two conclusions will never be simultaneously true or false (valid or invalid). So, it is called a complementary pair.

Conditions to check complementary pairs:

  • Both the conclusions should be individually false i.e. it should be invalid.
  • The entities (subject and object) of both the conclusions should be the same.
  • The conclusions should be in pairs of either / or, some or some not, some and no, and all and some not.
  • All and No will never form a Complementary Pair.

Types of Conclusion in Possibility

The table below shows all the possible conclusions which can happen in the possible case.

Types of Conclusion in Possibility

To be Converted into Definite Case

All (Universal Positive)

Example: All Black is being White is a Possibility

Some not (Particular Negative)

Converted into: Some Black are not White

Some (Particular Positive)

Example: Some Black being Beauty is a Possibility

No (Universal Negative)

Converted into: No Black is Beauty 

No (Universal Negative)

Example: No A being B is a Possibility

Some and No and No and Some are always a same possibility.

Some (Particular Positive)

Converted into: Some A are B

Some not (Particular Negative)

Example: Some A are not being B is a Possibility

All and some not and some not and All are always a same possibility

All (Universal Positive)

Converted into: All A are B

Note: -

  • If each, every, any, 100%, Name of Persons and etc words occurs in a positive way then they will be considered as ‘ALL’ and if these words occur in a negative way then they will be considered as ‘NO’.
  • If many, mostly, almost, little, few, and etc words occur in a positive way then they will be considered as ‘Some’ and if these words occur in a negative way then they will be considered as ‘some not’.
  • If ‘At least’ occurs in a conclusion then we have to ignore ‘At least’. Example: At least Some A are B. So, in this case we will consider Some A are B and will ignore At least.
  • If ‘Definitely’ occurs in a conclusion then we have to ignore ‘Definitely’. Example: Some P are Definitely Q. So, in this case we will consider Some P are Q and will ignore definitely.
  • If ‘Only’ occurs in a conclusion then we have taken ‘All’ in place of ‘Only’. Example: Only Mangoes are Sweet changes to All Mangoes are Sweet.

DU JAT mock test

DU JAT mock test

Points to Remember Before Solving Syllogism Questions

  • Syllogs are one of the most confusing parts of Reasoning but it becomes interesting if every concept of Syllogs gets clear to students.
  • The most important thing is that students should always consider statements 100% right.
  • And conclusion will only follow if it is 100% confirmed.
  • In conclusion, if there is any doubt about it, then the conclusion will not follow.
  • Be careful in case of possibilities, if there is doubt in any conclusion its possibilities may occur.
  • And if the conclusion is 100% sure, then its possibilities can’t happen.
  • Before solving syllogism, take a glance at directions of questions because sometimes in exams, syllogism of “does not follow” type comes.
  • By Keeping every point of our concept and important points, you will be easily able to solve questions of syllogism.

Syllogism Questions and Answers with Venn Diagrams PDF

There are some of the important Syllogism questions and their answers mentioned below for your practice and for understanding the tricks and unique methods to solve the Syllogism question easily.

Direction Question 1: Given questions contain four arguments of three sentences each. Choose the set in which the third statement is a logical conclusion of the first two.

(1) Some bikes are mopeds. All mopeds are scooters. some bikes are scooters

(2) All children are hairs. No hairs are red. No children are red.

(3) No pencil is a pen. Some pens are markers. Some pencils are markers.

(4) Every man has a wife. All wives are devoted. No devoted has a husband.

(a) (1), (2) and (3)

(b) (1) and (2).

(c) (3) and (2).

(d) (1), (2), (3), and (4)

Answer: (b) (1) and (2).

Explanation:

The first step to solve the syllogism question is that you should read the direction given in the question very carefully and understand the meaning of each and every word.

 And, in this question it is given that there are four arguments of three statements each.

And, we have to choose the set in which the third statement is a logical conclusion of the first two.

 Now, look at the first argument and find that the third statement is a logical conclusion of the first two or not.

  1. Some bikes are mopeds. All mopeds are scooters. some bikes are scooters

So, as we can see in the above Venn diagram that the third statement of the first argument is a logical conclusion of the first two statements i.e. some bikes are scooters.

 So, in this case the 1 conclusion follows.

 Now the second argument,

  1. All children are hairs. No hairs are red. No children are red.

As the statement says that no hairs are red and all children are hairs so it is evident that if all children are hairs and no hairs are red so the third statement no children are red follows because there is no relation between children and red also.

So, as we can see in the above Venn diagram that the third statement of the second argument is a logical conclusion of the first two statements i.e. No children are red.

So, in this case the 2 conclusions follow.

Now the third argument,

  1. No pencil is a pen. Some pens are markers. Some pencils are markers.

As the statement says that no pencil is pen and some pens are markers so it is evident that if no pencil is pen and some pens are markers so the third statement some pencils are markers does not follow because there is no relation between pencils and markers as given in the statements.

So, as we can see in the above Venn diagram, the third statement of the third argument is not a logical conclusion of the first two statements.

So, in this case the 3 conclusions do not follow.

So, after finding out the answers of all the three arguments we can use the elimination method. This method will help us to save time and we do not have to solve the fourth argument.

(a) So as per the options given we can easily eliminate the (a), (c), (d) options which have the (3) argument in their option and third argument does not follow so in that case the answer will be option (b) which says that option (1) and (2) follow which is true.

Direction Question 2: In the following question, statements are given followed by conclusions. You have to consider the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and decide which of the following conclusions logically follows from the given statements disregarding the commonly known facts. Select the conclusions that logically follows the given statements.

Statements:

Some wildlife’s are reserve

 All lands are forest

Some reserves are not forest

Conclusions:

  1. All lands can be reserve
  2. Some forest are not reserve

III. All forest are reserve

(a) Only I follows

(b) Both I and III follows

(c) Only II follows

(d) None of these

Answer: (d) None of these

Explanation:

We have to find the logical conclusions from the given statement.

Below you can see the Venn Diagrams made from the given statement.

We consider statements to be the exact truth. And we have to find the true or false or possibility conclusion from the given conclusions. If the conclusion result is true then it follows and if the conclusion result is false or possibility it does not follow.

The above Venn Diagrams are made according to the above mentioned statements.

Look at all the conclusions

  1. All lands can be reserve – It is a possibility so it can happen so, it is true means it follows.
  2. Some forests are not reserve – it is a definite case so, it is clear from the Venn Diagrams that some forests are reserve so , it is false means it does not follow.

III. All forests are reserve – again it is a definite case so, it is clear from the Venn Diagrams that All forests are not reserve so, it is false means it does not follow.

Now, as you can see the II and III conclusion is false and the subject and object of both the conclusions are the same but they do not form complementary pairs because there is no possibility of any one to be true so we have to take both in consideration.

So, the answer of this question will be I follow either II follows or III follows.

Direction Question 3: The question consists of two statements followed by two conclusions. Consider the statement to be true even if they vary with the commonly known facts and find out which of the given conclusion (s) logically follow(s) the given statements.

Statements:

Some discounts are borrowings

All borrowings are bargains

Conclusions:

  1. No bargain is a discount
  2. All bargains are discounts

(A) Either I or II follows

(B) Only I follows

(C) Both I and II follow

(D) Neither I nor II follows.

Answer: (D) Neither I nor II follows.

Explanation:

We have to find which of the given conclusion (s) logically follow(s) the given statements.

The above Venn Diagrams are made according to the above mentioned statements.

Now, we will see the conclusions.

  1. No bargain is a discount – it is a negative conclusion so, we will directly say it is false because it is a definite conclusion and there is nothing negative given in the statement.
  2. All bargains are discounts – As we can see in the Venn Diagram that some part of discounts are bargains but not all so, this conclusion is also false.

So, the answer will be neither I nor II follows.

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Direction Question 4: The question consists of two statements followed by two conclusions. Consider the statement to be true even if they vary with the commonly known facts and find out which of the given conclusion(s) logically follow(s) the given statement.

Statements:

All papers are words

Some words are letters

Conclusions:

  1. Some papers are letters
  2. No letter is a paper.

(A) Neither I nor II follows.

(B) Either I or II follows

(C) Both I and II follows

(D) Only II follow

Answer: (B) either I or II follows.

Explanation:

We have to find which of the given conclusion (s) logically follow(s) the given statements.

The above Venn Diagrams are made according to the above mentioned statements.

 Now, we will see the conclusions.

  1. Some papers are letters – the given conclusion is a possibility because there is nothing mentioned in the statement about papers and letters but there is a possibility so if the possibility is true then the conclusion is false so, this conclusion does not follow.
  2. No letter is a paper – Again it can be a possibility so if the possibility is true then the conclusion is false so, this conclusion does not follow.

But as you can see that the subject and object of both the conclusions are the same and both the conclusions are false and their possibilities are also true. And they are also forming complementary pairs.

They are complementary pairs because if the possibility of one of the conclusions is true then automatically the possibility of a second conclusion will be false and vice - versa. So, they satisfy all the conditions of either / or case.

Thus, the answer will be (B) either I or II follows.

Direction Question 5: The question consists of two statements followed by two conclusions. Consider the statement to be true even if they vary with the commonly known facts and find out which of the given conclusion(s) logically follow(s) the given statement.

Statements:

No problem is a solution.

All answers are solutions

Conclusions:

  1. Some answers are not problems
  2. All answers can be problems.

(A) Both I and II follows

(B) Either I or II follows

(C) Only I follows

(D) Neither I nor II follows

Answer: (C) Only I follow.

Explanation:

We have to find which of the given conclusion (s) logically follow(s) the given statements.

 The above Venn Diagrams are made according to the above mentioned statements.

 Now, we will see the conclusions.

  1. Some answers are not problems – in this conclusion it is given that some answers are not problems. It is a definite conclusion. And also it is mentioned in the statement that no problem is a solution. So, it is clear that if no problem is a solution then automatically some answers are not problems is a true conclusion because the second statement states that all answers are solutions if all the answers are and no solution can be a problem. Then this conclusion is true and it follows.
  2. All answers can be problems – it is a possibility but there is no possibility that All answers can be problems because we take statements as the true facts and in the statement it is clearly mentioned that All answers are solutions so we cannot change the statement. So this conclusion does not follow.

Therefore, the answer will be (C) Only I follow.

Direction Question 6: The question consists of two statements followed by two conclusions. Consider the statement to be true even if they vary with the commonly known facts and find out which of the given conclusion(s) logically follow(s) the given statement.

Statements:

All writings are typings

Some scripts are not tryings

Conclusions:

  1. Some writings are scripts
  2. Some typings are writings

(A) Only II follows.

(B) Both I and II follow.

(C) Only I follow.

(D) Neither I nor II follows.

Answer: (A) Only II follow.

Explanation:

We have to find that which of the given conclusion (s) logically follow(s) the given statements

 The above Venn Diagrams are made according to the above mentioned statements.

 Now, we will see the conclusions.

  1. Some writings are scripts – in this conclusion it is given that some writings are scripts but as per the statements we have made the above Venn Diagrams and the Venn Diagrams shows that there is no relation between writings and scripts. Thus, this conclusion is false and it does not follow.
  2. Some typings are writings – in this conclusion it is given that some typings are writings. This conclusion is true because the statement says that all writings are typings. So, if all writings are typings it is evident that obviously some typings will be writings. Therefore, this conclusion follows. 

Therefore, the answer will be (A) Only II follows.

Direction Question 7: The question consists of two statements followed by two conclusions. Consider the statement to be true even if they vary with the commonly known facts and find out which of the given conclusion(s) logically follow(s) the given statement.

Statements:

All files are folders

All folders are envelopes

Conclusion:

  1. Some envelopes are files
  2. Some files are envelopes.

(A) Only I follow.

(B) Only II follows

(C) Either I or II follows

(D) Both I and II follows

Answer: (D) Both I and II follow.

Explanation:

We have to find which of the given conclusion (s) logically follow(s) the given statements.

The above Venn Diagrams are made according to the above mentioned statements.

Now, we will see the conclusions.

  1. Some envelopes are files – This conclusion states that some envelopes are files. This conclusion is true because as we can see in the above Venn Diagrams that some parts of envelopes are files. So, this conclusion follows.
  2. Some files are envelopes – This conclusion states that some files are envelopes. This conclusion is also true because as we can see in the above Venn Diagrams clearly is that all files are envelopes. And the conclusion says that some files are envelopes so it is clear that if all files are envelopes then some files are envelopes is also true. So, this conclusion also follows.

Therefore, the answer will be (D) Both I and II follows.

Direction Question 8: In the question below are given two statements followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements:

All girls are beautiful

Some beautiful is intelligent.

Conclusions:

  1. Very few girls are intelligent.
  2. No girl is intelligent

(A) Only I follow

(B) Only II follows

(C) Either I or II follows

(D) Neither I nor II follows.

Answer: (C) Either I or II follows.

Explanation:

We have to find that which of the given conclusion (s) logically follow(s) the given statements

The above Venn Diagrams are made according to the above mentioned statements.

Now, we will see the conclusions.

  1. Very few girls are intelligent – This conclusion says that very few girls are intelligent. As we have already mentioned above, if words like few, little, mostly, almost and etc occur in the conclusion we will consider it as “Some or some not”. In this conclusion it is given in a positive way so we will consider it as some so, this conclusion changes in some girls are intelligent. The above Venn Diagrams clearly show that there is no relation between girls and intelligent so this conclusion does not follow. It is a false conclusion. 
  2. No girl is intelligent – This conclusion states that No girl is intelligent. As per the statements and the above made Venn diagrams clearly shows that there is no relation between girls and intelligent so this conclusion also will not follow. Thus, it is also a false conclusion.

But as you can see that the subject and object of both the conclusions are the same and both the conclusions are false and their possibilities are also true. And they are also forming complementary pairs.

They are complementary pairs because if the possibility of one of the conclusions is true then automatically the possibility of a second conclusion will be false and vice - versa. So, they satisfy all the conditions of either / or case.

Thus, the answer will be (C) either I or II follows.

Direction Question 9: In the question below are given two statements followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements:

All elephants are mammals.

All humans are mammals.

Conclusion:

  1. Some elephants are human.
  2. Some humans are not elephants.

(A) Only I follow.

(B) Only II follow.

(C) Either I or II follows.

(D) None follows.

Answer: (C) either I or II follows.

Explanation:

We have to find which of the given conclusion (s) logically follow(s) the given statement.

The above Venn Diagrams are made according to the above mentioned statements.

Now, we will see the conclusions.

  1. Some elephants are human – In this conclusion, it is given that some elephants are human. But as we see the Venn Diagrams made above which shows that there is no definite relation between elephant and human but it can be a possibility so we will consider this conclusion as false. So, it means that this conclusion does not follow.
  2. Some humans are not elephants – As we have already seen that there is no definite relation between human and elephant but we can consider it as a possibility so we have to take this conclusion as a false conclusion. So, it means that this conclusion also does not follow.

But as you can see that the subject and object of both the conclusions are the same and both the conclusions are false and their possibilities are also true. And they are also forming complementary pairs.

They are complementary pairs because if the possibility of one of the conclusions is true then automatically the possibility of a second conclusion will be false and vice - versa. So, they satisfy all the conditions of either / or case.

Thus, the answer will be (C) either I or II follows.

Direction Question 10: In the question below are given two statements followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements:

Some elephants are mammals.

No mammals are humans.

Conclusion:

  1. Some elephant are not human
  2. Some human are not elephant

III. All human can be elephant

(A) Only I follow.

(B) Only II follows.

(C) Either I or II follows.

(D) None of these.

Answer: (D) None of these.

Explanation:

We have to find which of the given conclusion (s) logically follow(s) the given statement.

The above Venn Diagrams are made according to the above mentioned statements.

Now, we will see the conclusions.

  1. Some elephants are not human – This conclusion is true. That means this conclusion follows because as we see the Venn diagrams it clearly shows that some elephants are mammals and no mammal is human. So, it means that some parts of elephants are also not humans. So, in that case this conclusion will follow.
  2. Some humans are not elephants – This conclusion is false. That means this conclusion does not follow because Human is an independent Venn diagram which does not have any relationship with elephants but elephant has a relation with human as we have mentioned in the first conclusion. But some humans who are not elephants can be a possibility so in that case also this conclusion does not follow.

III. All humans can be elephants – This conclusion is true that means this conclusion follows because in this conclusion it is clearly written that it can be so it is clear that this conclusion is a possibility.

Now you look at the Venn Diagrams drawn above that shows that there is a possibility of All humans can be elephants. So, this conclusion follows.

But the actual answer is both I and III follows.

But, this option is not available

So,

Therefore, the answer will be (D) none of these.