Syllogism Problems Solving | Reasoning Tips & Tricks

Syllogism is an important topic in logical reasoning that evaluates a candidate’s ability to draw conclusions from given statements. It is widely used in competitive exams like banking, SSC, campus placements, and other aptitude tests.

Understanding Syllogism

Syllogism consists of two or more statements, followed by conclusions. The task is to determine whether the conclusions logically follow from the given statements.

Types of Statements in Syllogism

1. Universal Affirmative (All A are B)
   • Example: All dogs are animals.
2. Universal Negative (No A is B)
   • Example: No cats are dogs.
3. Particular Affirmative (Some A are B)
   • Example: Some students are athletes.
4. Particular Negative (Some A are not B)
   • Example: Some cars are not electric.

Methods to Solve Syllogism Problems

1. Using Venn Diagrams

• The most effective way to solve syllogism problems is by drawing Venn diagrams.
• Represent each statement visually and observe possible relationships.
• Identify the overlapping or separate sections to determine whether the given conclusions are valid.

2. Applying Standard Rules

Understanding standard deduction rules can help in solving problems quickly.

• Rule 1: All + All = All
  • Example:
    • Statement 1: All apples are fruits.
    • Statement 2: All fruits are healthy.
    • Conclusion: All apples are healthy.
• Rule 2: All + Some = No Conclusion
  • Example:
    • Statement 1: All cats are animals.
    • Statement 2: Some animals are wild.
    • Conclusion: No valid conclusion can be drawn.
• Rule 3: Some + Some = No Conclusion
  • Example:
    • Statement 1: Some men are doctors.
    • Statement 2: Some doctors are teachers.
    • Conclusion: No conclusion can be drawn between men and teachers.
• Rule 4: No + All = Some Not
  • Example:
    • Statement 1: No birds are mammals.
    • Statement 2: All mammals are animals.
    • Conclusion: Some animals are not birds.

3. Understanding Complementary Pairs

Complementary pairs help in determining the correctness of conclusions.

• If one conclusion is false, the other must be true.
• Example:
  • Given the statement “Some A are B,” its complementary statement is “Some A are not B.”

4. Avoid Assumptions

• Do not rely on real-world knowledge; only base conclusions on given statements.
• If a statement does not explicitly state a relationship, do not assume it.

Example Questions on Syllogism

Question 1

Statements:

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

Conclusions:

1. Some mangoes are sweet.
2. Some sweet things are fruits.

Solution:

• Drawing a Venn diagram shows that “Some mangoes are sweet” is not a valid conclusion, as there is no direct relation given between mangoes and sweetness.
• “Some sweet things are fruits” is valid because some fruits are sweet.
• Answer: Only Conclusion 2 follows.

Question 2

Statements:

1. All books are papers.
2. Some papers are newspapers.

Conclusions:

1. Some newspapers are books.
2. Some papers are books.

Solution:

• The first conclusion is incorrect because there is no direct relationship between newspapers and books.
• The second conclusion is correct because some papers include books.
• Answer: Only Conclusion 2 follows.

Common Mistakes to Avoid

1. Misinterpreting Statements
   • “Some” does not mean “All.”
   • “No” does not imply “Some Not.”
2. Skipping Venn Diagrams
   • Many students try to solve questions mentally, which increases the chances of errors.
3. Assuming Real-World Logic
   • Always base your answers strictly on the given statements, not general knowledge.