How to Solve: CUET Reasoning – Syllogisms (Venn Diagram Method)

How to Solve: CUET Reasoning – Syllogisms (Venn Diagram Method)

Introduction

"Imagine this: You’re in the CUET exam, staring at a syllogism question—three statements, five options, and 90 seconds left. One wrong move, and you lose marks. But if you master the Venn Diagram method, you’ll solve it in under 30 seconds—guaranteed. Let’s break it down."

What You Need To Know First

1. Basic logical statements – Understand "All," "Some," "No," and "Some not."
2. Set theory basics – Know how circles (sets) overlap in Venn diagrams.
3. Deductive reasoning – Follow a structured approach to eliminate wrong answers.

Key Vocabulary

Formulas To Know

(No algebraic formulas—just logical rules to memorize.)

1. "All A are B" → A is entirely inside B (small circle inside big circle).

2. MEMORIZE THIS: If "All A are B," then "Some B are A" is also true.

3. "No A are B" → A and B do not overlap (separate circles).

4. MEMORIZE THIS: If "No A are B," then "No B are A" is also true.

5. "Some A are B" → A and B overlap (circles intersect).

6. MEMORIZE THIS: "Some A are B" does not mean "Some A are not B."

7. "Some A are not B" → A extends outside B (part of A is separate).

8. MEMORIZE THIS: This does not mean "No A are B."

Step-by-Step Method

Step 1: Identify the Premises and Conclusion

• Read the question carefully.
• Underline the two premises and the conclusion.

Step 2: Draw the First Premise as a Venn Diagram

• Start with the universal statement (if any).
• Example: "All A are B" → Draw a small circle (A) inside a larger circle (B).
• If no universal statement, start with the first premise.

Step 3: Add the Second Premise to the Same Diagram

• Overlay the second statement on the first diagram.
• Example: "Some B are C" → Draw a third circle (C) overlapping with B.
• If the second premise is "No B are C," draw C separate from B.

Step 4: Check the Conclusion Against the Diagram

• Look at the conclusion and see if it must be true based on the diagram.
• If the conclusion does not match, it is invalid.
• If it matches, it is valid.

Step 5: Eliminate Wrong Options

• Compare the conclusion with the given options.
• Cross out any option that does not match the diagram.

Step 6: Verify with All Possible Cases

• If unsure, test all possible overlaps to confirm the conclusion holds.

WORKED EXAMPLE (Using the Steps)

Example 1 – Basic

Premises: 1. All dogs are animals. 2. All animals are living things. Conclusion: All dogs are living things.

Step-by-Step Solution: 1. Identify premises:
- Premise 1: All dogs are animals.
- Premise 2: All animals are living things.
- Conclusion: All dogs are living things.

1. Draw Premise 1:

2. Draw a small circle (Dogs) inside a larger circle (Animals).

3. Add Premise 2:

4. Draw an even larger circle (Living Things) around Animals.

5. Check conclusion:

6. Dogs (smallest circle) is inside Living Things (largest circle).
7. Conclusion is valid.

What we did and why: - We layered the circles to show inclusion. - The conclusion must be true because dogs are a subset of animals, which are a subset of living things.

Example 2 – Medium (With "Some")

Premises: 1. Some students are athletes. 2. All athletes are disciplined. Conclusion: Some students are disciplined.

Step-by-Step Solution: 1. Identify premises:
- Premise 1: Some students are athletes.
- Premise 2: All athletes are disciplined.
- Conclusion: Some students are disciplined.

1. Draw Premise 1:

2. Draw two overlapping circles (Students and Athletes).

3. Add Premise 2:

4. Draw a larger circle (Disciplined) around Athletes.

5. Check conclusion:

6. The overlapping part of Students and Athletes is inside Disciplined.
7. Therefore, some students must be disciplined.
8. Conclusion is valid.

What we did and why: - We showed that the overlapping part (some students who are athletes) is inside the disciplined circle. - The conclusion must be true because those students are part of the disciplined group.

Example 3 – Exam Style (Tricky)

Premises: 1. No birds are mammals. 2. Some mammals are pets. Conclusion: Some pets are not birds.

Step-by-Step Solution: 1. Identify premises:
- Premise 1: No birds are mammals.
- Premise 2: Some mammals are pets.
- Conclusion: Some pets are not birds.

1. Draw Premise 1:

2. Draw two separate circles (Birds and Mammals).

3. Add Premise 2:

4. Draw a third circle (Pets) overlapping with Mammals.

5. Check conclusion:

6. The part of Pets that overlaps with Mammals does not overlap with Birds.
7. Therefore, some pets are not birds.
8. Conclusion is valid.

What we did and why: - We showed that pets that are mammals cannot be birds (since no birds are mammals). - The conclusion is necessarily true based on the diagram.

Common Mistakes

Exam Traps

1-Minute Recap

"Okay, let’s do a lightning recap—perfect for last-minute revision.

1. Read carefully: Underline the two premises and the conclusion.
2. Start with "All" or "No": Draw the universal statement first.
3. Add the second premise: Overlay it on the same diagram.
4. Check the conclusion: Does it have to be true? If yes, it’s valid.
5. Eliminate wrong options: Only pick what the diagram proves.

Remember: - "All A are B" = A inside B. - "No A are B" = Separate circles. - "Some A are B" = Overlapping circles. - "Some A are not B" = A extends outside B.

If you follow these steps, you’ll solve syllogisms faster than the clock. Good luck—you’ve got this!