# How to solve Syllogism Problems Quickly with Examples

Syllogism Questions in Reasoning are mostly asked in all the top competitive exams. In syllogism questions, a few statements with some conclusions are asked to judge the candidates ability of determining the right conclusion. Syllogism is a part of Reasoning and a science of thoughts. Syllogism is also referred to ‘Logic’. Since syllogism is an important part of reasoning, so a working knowledge of its rules is required for the candidate to remember.

Here is a syllogism statement.
All cats are dogs.
This type of statement is called universal affirmative statement. You can solve these question using venn diagrams. But most of the candidates find it difficult to solve syllogism questions using venn diagrams.
But don’t bother, here, I am providing you few tricks to solve these syllogism  questions. To solve these questions, you need to remember some rules.

All cats are dogs.

Now here ‘all’ is qualifier. Similarly if some or no is given, then some or no will be qualifiers.
‘Cat’ is subject- subject is the word of which something is said.
‘Dogs’ is predicate- predicate is a part of the preposition which is affirmed or denied about the subject.
‘are’ is cupola- cupola is the word which denotes the relationship between subject and predicate.

Here are the basic conversions that are needed to be remembered while solving syllogism questions.
For example, here is a statement:
All cats are dogs.
Now remember
‘All’ can be converted to ‘some’ only
So the conclusion that can be drawn from the above statement is that

Some dogs are cat.

So here are three types of basic statements that are asked in exams
All dogs are cats.
Some dogs are cats.
No dogs are cats.

Conversions to remember on reversing the statement
For example-all dogs are cat-
On reversing  it-some cats are dogs.

So here is the conversions or conclusions  to remember while the statements are reversed and alone.
Table 1 to remember
{      ‘all’ can be converted to ‘some’
‘some can be converted to ‘some’ .
‘no’ can be converted to ‘no’.                }……………….Table 1

For example
Some dogs are cats
Can be converted to
‘Some cats are dogs’- this is the conclusion of ‘some dogs are cats’ statement.

Similarly
No dogs are cats
Can be converted to
No cats are dogs.

But when two or more statements are given, which are mostly in all types of exams.
We also have to combine the statements and derive out the conclusions other than deriving out individual conclusions of the statements like the ones given above. For those questions, we have to remember the Table 2 given below…
Table 2 to remember
{      All +all= all
All +no= no
All + some= no conclusion
Some + all = some
Some + not=some not
Some + some=no conclusions
No + all=some not reversed
No + some=some not reversed
No + no=no conclusion
Some not+ anything= no conclusion
Some not reversed + anything= no conclusion  }                              ……………….Table 2

So here is an example.
Question:1
{
Statements:
All mangoes are chairs.
Some chairs are oranges.
Conclusions:
I-                    All mangoes are oranges.
II-                  Some oranges are mangoes.
III-                No mango is an orange.
}

We have to combine the first part (Qualifiers) i.e. “all, some, no”  of every statement to derive out some conclusions. Also we have to cancel ‘chairs’ from both sides.
Remember we have to arrange the statements such that we can cancel predicate from the first statement and subject from the second statement. So the predicate from the first statement and subject from the second statement should be same name. mostly it is given in the question but if it is not so, then we should try to reverse the statement as discussed above.
So the statements should be like the one given above:
Statements
1.       All mangoes are chairs.
+
2.       Some chairs are oranges.

Here in the above statement ‘chair’ is predicate in the first statement and subject in the second statement. So we can cancel it and combine the qualifiers of the above statements.

i.e. combining all + some. The answer will be no conclusion. Because all and some, when combined gives no conclusion. This addition is given in the table 2.
Also by converting the statements individually as per the table 1 i.e. on reversing the statements
We get the following conclusions
{    All chairs are mangoes.(because all can be converted to some)
Some oranges are chairs.(because some can be converted to some)       }
So the above conclusions does not match the conclusions given in the question above.
Hence no conclusion is the answer of the question.

Now we will discuss another example
{    Statements
All homes are schools.
All schools are colleges
Conclusions
All homes are colleges.
Some homes are not colleges.               }

Solution:  cancelling ‘schools’ from both the statements as discussed above, we combine all and all (Qualifiers) of both statements as per Table 2.
All + all = all
So after cancelling ‘school’ and joining all and all, we get the below statement.
‘All homes are colleges’
So Conclusion I is true.
Also by reversing both the statements as per table 1, we get the below conclusions.
( upon reversing statement 1, we get the conclusion- some schools are homes.
upon reversing statement 2, we get the conclusion - All colleges are schools  )
so none of these conclusions follows the conclusions given in the question’s conclusions.
So only conclusion 1 follows.------------answer

Question-3. Special cases
Statements
I.                    All vegetables are green.
II.                  Some greens are fruits.
Conclusions
I.                    Some fruits are vegetables.
II.                  No fruits is vegetable.

Solution:
Now in this question, cancelling green from both given statements, and adding both statements.
All+ some = no conclusion                        ………as per Table 2.
Now reversing the statements or converting the table as per Table 1 given above.
None of the conclusions given in the question can match upon reversing as per Table 1 because the conclusions are given as the normal combination of both the statements.
So what should be done.
Now here is the idea.
Combine both statements and cancel the predicate( green ), we get the conclusion
All+ some= no conclusion=  some and no should be applied to the question.
All+ some= no conclusion= (all + some= no conclusion= ‘some’ and ‘no’) fruits is/are vegetable(s)----no conclusion should be converted as the combination of the statements and with application of some and no to the conclusion.

So the conclusion should be
Some fruits are vegetables
And
No fruits are vegetables

After the application of ‘some’ and ‘no’ to the statements addition, the answer is
Either ‘some fruits are vegetable’ follows
Or ‘No fruits is a vegetable’ follows

So in those questions, in which ‘no conclusion’ comes as a combination of the statements, try to apply ‘some’ and ‘no’ to the statements and find the conclusions in the given question whether they match.
So in the above question 3 of special case- The answer should be-
Either conclusion I follows or conclusion II follows.