Syllogisms is one of the main topics in Verbal or Logical Reasoning in various competitive exams like SBI PO, IBPS PO, SBI Clerk, IBPS Clerk, SBI Associate PO, CAT, IBPS RRB, SSC CGL, NICL AO, NIACL AO, LIC AAO, etc. Generally 5-6 questions are asked on this topic alone in each of these exams. As it is an important, easy and scoring topic, you should have good command over it. Follow some basic concepts and rules explained in this first article of the series, and you can easily solve these types of questions in just a few seconds.
Syllogisms often appears as a part of Logical Reasoning or Verbal Reasoning. It consists of some premises (statements) and one or more conclusions. The conclusions are derived from the given statements. The statements and conclusions may often seem to be illogical or go against what we know to be facts according to our daily lives. But we MUST assume the statements to be true. Whether the conclusion is true or not in the context of the true statements given, is what the question is about in syllogisms.
“All mangoes are toys” is a statement which looks weird, but must be taken to be true, if given as a statement/premise.
This statement alone, or with other such related statements, can lead to a conclusion such as “Some toys are mangoes.”
In such kinds of problems, you need to find out what will definitely be true, and what can be possibilities.
These kinds of problems can be easily solved by Venn Diagrams. While doing so, try to correlate the explanations with what you see in the diagrams.
Venn Diagrams are a way to represent sets of objects and picturize the relations between a collection of objects as given in a set of statements. They are often shown as circles and labelled. It shows all the definite or logical relations between the collection of statements.
Based on this statement alone, we can conclude some things definitely and some things as a possibility. Definite statements are those that are certainly true based on the statement(s) given. These are those that can most certainly be concluded on the basis of the Least Venn Diagram.
NOTE: The Least Venn Diagram shows minimal or least possible overlapping between two groups. These are the most common ways of representing the given statement. Each selection has its own unique Least Venn Diagram.
Possibilities are those that may be true but are not definite. They can be shown using either the Least Venn Diagram or Alternate Venn Diagrams. Alternate Diagrams are those Venn Diagrams that are not commonly used to depict that particular statement, but are also valid ways of representing the statement. Note that Alternate Venn Diagrams are not always correct all the time, but can often be useful in proving something wrong.
There are four categories you must remember. These tell you how many objects have a certain attribute or how many you have selected. You can select:
- All (i.e. you can select every object in the group.)
- Some (i.e. you can select a few objects in the group.)
- None (i.e. you can leave out all objects in the group.)
- Some Not (i.e. you can leave out a few objects in the group.)
Statement:- All A are B
What does this mean? Every object of Type A is also an object of Type B. You can pick any object in A and it will definitely lie in B.
|i. Some A are B.||(Refer fig.2) If we select even some of the objects of Type A, they will still lie inside B.|
|ii. Some B are A.||(Refer fig. 2) Some objects of Type B are also of Type A – those that lie in both A and B.|
NOTE: Some A are B DOES NOT MEAN that some A are not B because as seen from the fig. 2, there are no objects of Type A that are not of Type B.
|i. All B are A.||(Refer fig.4) When all A are B, and when all B are A, clearly, the two groups are the same i.e. the two groups overlap completely.|
|ii. Some B are not A.||(Refer fig. 3) We do not know for sure if there are some B that are not A. But there is a possibility of it.|
Statement:- Some A are B
What does this mean? There are a few objects in A that are also in B.
|Some B are A.||(Refer fig.5) There are some objects of Type A that are of Type B. Then definitely we can say that these B are A.|
|i. All B are A.||(Refer fig.6) Some A are B can also mean that every object of type B lies in A.|
|ii. Some A are not B.||(Refer fig. 7) We know that some A are definitely B. There is a chance that there are some A that are not common with B, and these will lie in the area outside B, but inside A|
|iii. All A are B.||(Refer fig. 8) When all A are B, it is then definite that whatever group of A you pick, it will definitely be in B. So if all A are B, then definitely some A are B.|
|iv. Some B are not A.||(Refer fig. 9) Like in case ii, we know that some A are definitely B. But there is a chance that there are some B that are not common with A, and these will lie in the area outside A, but inside B.|
Statement:- No A are B.
What does this mean? When we are sure that there is nothing in A that is common with B, we say that no A are B.
|i. No B are A.||(Refer fig.10) When there is nothing in common between A and B, then no B can be A.|
|ii. Some A are not B.||(Refer fig.10) If no A is B, then definitely we can also say that some A are not B. This is because if we select any group of objects from A, then they will definitely not lie in B.|
|iii. Some B are not A.||(Refer fig.10) The reason is same as in case ii.|
|—||There are no possibilities that can be drawn from this case. All conclusions are definite in relation to A and B.|
4. SAME NOT
Statement:- Some A are not B.
What does this mean? We are sure that there are some objects of Type A that are not of Type B.
|—||(Refer fig.11) No definite conclusion can be drawn on the basis of this statement alone.|
|i. All B are A.||(Refer fig.12) In the case where all B are A, there could be some objects of Type A that lie outside B. These A are not B. So our statement that Some A are not B holds true.|
|ii. Some A are B.
Some B are A.
|(Refer fig. 13) When we know that there is some overlap between A and B (shown as dots in fig 13), and there are some objects that lie outside B but inside A (shown as dashes in fig 13), we can say that some A are not B, and the statement holds true.|
|iii. Some B are not A.||(Refer fig. 14) When we have some overlap between A and B, and there are some objects in A that don’t lie in B and some objects in B that don’t lie in A, we can see that both the statement and this possibility holds true.|
|iv. No A are B.
No B are A.
|(Refer fig. 15) When there is no object in common between A and B, we can see that any group of objects of Type A you take will not lie in B. So we can say that some A are not B. Note that we are not saying that some A are B.|