Tips To Solve Syllogisms

Tips to Solve SyllogismsThe syllogism is a topic in the reasoning part which is a very important section in most of the competitive exams like the bank exams, railways, SSC, etc. This topic i.e. the syllogism generally has very high weightage in the reasoning section and thus has become very important for the exam.

The syllogisms are just argument sentences that require deductive reasoning to arrive at some conclusions. Presently, the SBI and IBPS exams ask the syllogism questions in a reversed way i.e. statements are asked from the given conclusions.

In this article, some examples are provided for the most common types of syllogism questions along with the Venn diagrams to solve them with ease.

  1. All A are B

This phrase simply 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:

 All A are B

In this diagram it is clearly visible that circle A is inside the circle B which simply means that B contains the entire A i.e. All A are B.

  1. A = B

In this case, the conclusion 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”. This means A is a subset of B and B is also a subset of A. The Venn diagram is:

A = B

Here A is contained in B and so is B contained in A. So, here A contains all B and again B also contains all A.

  1. No A are B

It is simply understandable 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:

No A are B

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.

  1. Some A are B

This is the case when some of A is in B that is A and B are intersecting and thus some B are A will also be true. The Venn diagram depiction is as:

Some A are B

Here the shaded portion simply indicates that some portion of A is contained in B while the unshaded portion is uncertain portion and does not indicate anything whether A is contained in B or not.

  1. Some A are not B

This 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;

Some A are Not B

In this, some portion of A is surely not included in B while there is no surety whether the shaded 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” sentence will always imply an “All” conclusion.
  2. Any “All’ and “No” sentence will always imply a “No” conclusion.
  3. Any ‘All” and “Some” sentence will always imply a “No” conclusion.
  4. Any “Some” and “All” sentence will always imply a “Some” conclusion.
  5. Any “Some” and “No” sentence will always imply a “Some not’ conclusion.
  6. Any “Some” and “Some” sentence will always imply a “No” conclusion.

Tips to solve the questions related to Syllogism:

  1. Read the question thoroughly
  2. Start drawing the Venn diagram
  3. Follow the sequence of the question while drawing
  4. Analyze the conclusion from the Venn diagram
  5. Check for other alternative solutions at the end.

Example:

Statements:

  1. Some pencils are dogs
  2. All dogs are pens
  3. All pens are cats

Conclusions:

  1. All dogs are cats
  2. Some pens are pencils
  3. Some pencils are cats

Solution:

Analysing the first statement, the Venn diagram can be made as;

Now as per the second statement, all dogs are pens, we can draw the Venn diagram as:

Now as per the last statement which says that all pens are cats, we get

This is the total representation of the statements. Now the conclusion needs to be analyzed one by one.

For the first conclusion, it is seen that the circle dogs is engulfed inside the circle cats. Thus the conclusion “all dogs are cats” is true.

For the second conclusion, the circles pens and pencils intersect each other and hence, the conclusion “some pens are pencils” is also true.

For the third conclusion, the circles cats and pencils also intersect each other and hence the conclusion “some pencils are cats” is also true.

Therefore all the conclusion in this question is true.

In this way, the questions related to syllogism can be easily solved. The only thing that is important is to practice different variations of syllogism related questions so as to gradually build up the confidence.