The document Basic Concept: Syllogisms & Explained with Examples LR Notes | EduRev is a part of the LR Course Logical Reasoning (LR) and Data Interpretation (DI).

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Syllogism is a form of reasoning in which a conclusion is drawn from two or three given propositions or statements. It uses deductive reasoning rather than inductive reasoning. You have to take the given statements to be true, even if they are at a variance from established facts.

Let us see an example of deductive reasoning.

Statements:

A. All cats are dogs.

B. All dogs are birds.

Conclusion â€“ All cats are birds.

This conclusion is quite visible. But to solve complex problems we have some standard methods.**Method 1- Analytical Method**

Following are the four major types of statements generally asked:

Sr. No. | Type of statement | Represented by the letter | Example |

1 | Universal Positive | A | All boys are handsome |

2 | Universal Negative | E | No girl is clever |

3 | Particular Positive | I | Some rats are dogs |

4 | Particular Negative | O | Some ships are not planes |

While deriving conclusions, following points should be kept in mind:

- With two particular statements, no universal conclusion is possible.
- With two positive statements, no negative conclusion is possible.
- With two negative statements, no positive conclusion is possible.
- With two particular statements, no conclusion is possible, except when an 'I' type of statement is given and then by reversing it, an 'I' type of conclusion is given.

**Important points related to conclusions drawn from single statements.**

- A statement of type 'E' when reversed, gives a conclusion of type 'E & O'.
- A statement of type 'A' when reversed, gives a conclusion of type 'I'.
- A statement of type 'I' when reversed, gives a conclusion of type 'I'
- A statement of type 'O' when reversed, does not give a conclusion of any type.

**Method 2- Venn Diagrams**

Another method of solving such type of questions is by drawing Venn diagram representing the statements. However, it is important that all possible Venn diagrams be drawn. If a conclusion can be deduced from all the possible solutions then that conclusion is true. If the conclusion can be concluded from one of the possible Venn diagram and not from the other possible Venn diagram then that conclusion is taken as false.**Solved Examples****Example1:Which of the two conclusions can be concluded on the basis of given statements?**

- Statements:
- Some parrots are scissors.
- Some scissors are not combs.
- Conclusions:
- Some scissors are parrots.
- Some combs are parrots.

**Solution: **Now, in this case, the possible conclusion is: Some scissors are parrots (I to I), as the universal principal no. 4 says, that with two particular statements only I to I is possible. Therefore, only 1 conclusion is possible. Nothing else is possible.

**Example 2 : Which of the two conclusions can be concluded on the basis of given statements?**

- Statements:
- All flowers are candles.
- All lanterns are candles.
- Conclusions:
- Some flowers are lanterns.
- Some candles are lanterns.

**Solution:**

Three possible diagrams are shown above for the given statements.

Conclusion I follows from last two possible solutions, but does not follow from the first

possible solution. Therefore, this conclusion is false.

Conclusion II follows from all the three possible solutions.

Therefore, conclusion II is true.**Example 3: Which of the two conclusions can be concluded on the basis of given statements?**

- Statements:
- All prisoners are men.
- No man is educated.
- Conclusions:
- All prisoners are uneducated.
- Some men are prisoners.

**Solution: **Two possible diagrams are shown below for the given statements.

Conclusion I follows from both the possibilities, so conclusion I is true.

Conclusion II also follows from both the possibilities, so conclusion II is also true.

Therefore, both conclusions are true.**Example 4: Which of the two conclusions can be concluded on the basis of given statements?**

- Statements:
- All sides are lengths.
- No length is a breadth.
- Conclusions:
- All lengths are sides
- No breadth is a side

**Solution: **Two possible diagrams are shown below for the given statements.**Conclusion I: **False (conclusion follows from the second possibility but doesn't follow from the first possibility)**Conclusion II: **True (conclusion follows from both the Venn diagram possibilities.)

Therefore, only conclusion II is true.

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