# How to solve Venn Diagrams in LR?

Result Date: 4th Jan 2020 The Logical Reasoning section includes a set of questions that require the use of Venn Diagrams. Mathematically, Venn Diagrams are essentially are a way to represent sets and perform set operations. In simpler terms, a Venn diagram uses overlapping circles to organize things and highlight how the things are similar or different. Venn diagrams help to visualise the given data clearly and derive the right conclusions from it. A simple example of a Venn diagram is given below:

• All cats are dogs

Socrates is a cat The conclusion derived from looking at the Venn diagram is that since all cats are dogs and Socrates is a cat, therefore, Socrates is a dog. The Venn diagram depict each item in the statement and highlight the relationship between them, thus, making the job of decoding the conclusion simpler.

### 1. How to solve Venn Diagram?

Using Venn diagram is the most effective way to solve a lot of Statement-Conclusion questions as well as questions based on sets. It is important that you learn to identify the terms in the statement and the relationship between them, which can help you draw a Venn diagram and get to the conclusion.

• The idea is to capture the given information by using circles. Here, first draw a circle depicting the larger item. And then move inwards to represent the other terms. For instance, to draw a Venn diagram that best depicts the relation between Men, Fathers and Engineers, we would first identify the larger item in this statement, that is, Men, followed by fathers and engineers. Hence, the Venn diagram shall be: What the above Venn diagram tells us is that some men are fathers and some engineers. All fathers are men and some fathers are engineers. However, not all engineers are men.

• In case of particular statements that do not include the entire set, there will always be overlapping between the circles. For instance, Some taxis are cabbies. Some cabbies are Mercedes. Some taxis are Mercedes.

The Venn Diagram for this will be overlapping circles, ### 2. Venn diagram and Syllogism

Venn diagram is particularly useful to tackle Syllogisms.

• Let’s consider some possibilities.

1. Some A's are B Definite Conclusions

• Some A is B
• Some B is A

Possible Conclusions

• All A’s are B
• All B’s are A
• Some A are not B
• Some B are not A

2. All A's are B Definite Conclusion

• All A is B
• Some A is B
• Some B is A

Possible Conclusions

• All B’s are A
• Some B’s are not A

3. No A is B Definite Conclusion

• No A is B
• No B is A
• Some A is not B
• Some B is not A

4. Some A's are not B Definite Conclusion

• Some A’s are not B

Possible Conclusion

• Except All A’s are B, all other possibilities follow

Keep in mind the following rules while using Venn diagram

• Draw the Venn diagram based on the statement given and the terms in the statement
• If the definite conclusion doesn’t satisfy the Venn diagram, then there is no need to check the possible conclusions
• If the definite conclusion does satisfy the Venn diagram, then it must satisfy all possible conclusions