How to Solve Syllogism Problems | Reasoning Tricks & Tips

How to Solve Syllogism Problems | Reasoning Tricks & Tips

How to Solve Syllogism Problems | Reasoning Tricks & Tips

Syllogism problems are a crucial part of logical reasoning in competitive exams and placement tests. These questions test your ability to deduce conclusions from given statements using logical relationships. Let’s break down the process of solving syllogism problems efficiently.

Understanding Syllogism

A syllogism consists of two or more statements (premises) followed by conclusions. Your task is to determine which conclusions logically follow from the given statements.

Types of Statements in Syllogism:

  1. Universal Affirmative (All A are B)
    • Example: All cats are animals.
    • Meaning: Every cat belongs to the category of animals.
  2. Universal Negative (No A is B)
    • Example: No birds are mammals.
    • Meaning: There is no overlap between birds and mammals.
  3. Particular Affirmative (Some A are B)
    • Example: Some dogs are pets.
    • Meaning: At least one dog belongs to the category of pets.
  4. Particular Negative (Some A are not B)
    • Example: Some cars are not electric vehicles.
    • Meaning: At least one car does not belong to the category of electric vehicles.

Steps to Solve Syllogism Problems

Step 1: Identify the Given Statements

Carefully read the statements and categorize them as universal affirmative, universal negative, particular affirmative, or particular negative.

Step 2: Draw Venn Diagrams (if needed)

Using Venn diagrams helps visualize relationships between different elements.

  • Use circles to represent different categories.
  • Overlapping circles indicate shared members between two categories.
  • Non-overlapping circles indicate no relationship.

Step 3: Analyze the Given Conclusions

Compare the given conclusions with the Venn diagram.

  • If a conclusion follows logically from the statements, it is true.
  • If it does not follow logically, it is false.
  • If it may or may not be true, it is considered “Can’t be determined”.

Step 4: Apply Logical Rules

If drawing Venn diagrams is time-consuming, use the “No Conclusion” and “Either/Or” rules:

  • If some A are B is true, some B are A is also true.
  • If all A are B and all B are C, then all A are C.
  • If two conclusions contradict each other, one must be false.

Examples and Solutions

Example 1: Basic Syllogism

Statements:

  1. All apples are fruits.
  2. Some fruits are sweet.

Conclusions:

  1. Some apples are sweet.
  2. All fruits are apples.

Solution:

  • Using a Venn diagram, we see that “apples” are inside “fruits,” but we have no information about the sweetness of apples. So, Conclusion 1 is false.
  • Not all fruits are apples; some fruits may be oranges, bananas, etc. So, Conclusion 2 is also false.

Example 2: Using the “Either/Or” Rule

Statements:

  1. Some books are papers.
  2. No papers are pens.

Conclusions:

  1. Some books are not pens.
  2. All books are pens.

Solution:

  • We know some books are papers and no paper is a pen, so some books might not be pens.
  • Conclusion 1 may be true, but it’s not explicitly stated, so it’s uncertain.
  • Conclusion 2 is false because we cannot say all books are pens.

Example 3: Universal Affirmative Statements

Statements:

  1. All dogs are animals.
  2. All animals are living beings.

Conclusions:

  1. All dogs are living beings.
  2. Some living beings are dogs.

Solution:

  • From Statement 1, dogs are a subset of animals.
  • From Statement 2, animals are a subset of living beings.
  • Since dogs are within animals, which are within living beings, all dogs are living beings (Conclusion 1 is true).
  • If all dogs are living beings, it means some living beings (at least dogs) are dogs (Conclusion 2 is also true).

Correct Answer: Both conclusions follow.

Example 4: Universal Negative Statements

Statements:

  1. No cat is a dog.
  2. All dogs are mammals.

Conclusions:

  1. No cat is a mammal.
  2. Some mammals are not cats.

Solution:

  • Statement 1 says that there is no relationship between cats and dogs.
  • Statement 2 tells us that all dogs belong to the category of mammals.
  • Conclusion 1 (No cat is a mammal) is false because we only know that cats and dogs are separate, but we don’t have information about whether cats are mammals or not.
  • Conclusion 2 (Some mammals are not cats) is true because all dogs are mammals, and we know that dogs are not cats, so at least some mammals (dogs) are not cats.

Correct Answer: Only Conclusion 2 follows.

Example 5: Particular Statements

Statements:

  1. Some students are girls.
  2. Some girls are intelligent.

Conclusions:

  1. Some students are intelligent.
  2. Some intelligent people are girls.

Solution:

  • We know some students are girls and some girls are intelligent, but there is no direct connection between students and intelligence in the given statements. So, Conclusion 1 does not follow.
  • Conclusion 2 (Some intelligent people are girls) is true because it is directly stated in Statement 2.

Correct Answer: Only Conclusion 2 follows.

Conclusion

Syllogism problems consist of two premises followed by conclusions. Read the premises carefully to identify the subjects, predicates, and the relationship between them. Use Venn diagrams to visually represent the relationships between different sets. This can help you quickly identify valid conclusions by visually analyzing the overlap between the sets.

How to Solve Syllogism Problems | Reasoning Tricks & Tips