How do 'some A are B' and 'some A are not B' work together?

'Some A are B' means at least one A is a B. It does not tell you about the rest of A, so 'some A are not B' may or may not be true. Treat them as separate facts — never assume one from the other unless the diagram forces it.

What are possibility-based conclusions?

Some questions ask whether a conclusion 'can be true' (possibility) rather than 'must be true'. A possibility conclusion follows if there exists at least one valid diagram where it holds. This is the opposite test from the definite-conclusion rule.

How do 'either-or' conclusions arise?

When two conclusions individually do not follow, but in every diagram at least one of them is true, and they are complementary (e.g., 'Some A are B' and 'No A are B' about the same pair), the answer is 'either I or II follows'.

Syllogisms — Statements, Conclusions & Venn Method | TNPSC, SSC, Bank

Quick Concept Summary

Syllogisms give you statements (premises) and ask which conclusions logically follow. The reliable method is Venn diagrams: translate each statement into circles, then test each conclusion against every possible arrangement. The golden rule — a conclusion follows only if it is true in all possible diagrams — removes all guesswork.

Translating Statements to Diagrams

Statement	Diagram
All A are B	A circle fully inside B
No A are B	A and B separate (disjoint)
Some A are B	A and B overlap
Some A are not B	part of A lies outside B

The Method (4 steps)

1. Draw the definite statements first (All, No). 2. Add the flexible ones (Some) in the way the question allows. 3. Try to draw a diagram that breaks the conclusion. 4. If you cannot break it in any valid diagram → it follows. If you can → it does not follow.

Special Cases

Possibility ("can be true"): follows if at least one valid diagram supports it.
Either–Or: when neither conclusion alone always holds, but one of two complementary conclusions is always true.
Some A are B ⇒ Some B are A (this reverse always holds).
All A are B ⇒ Some B are A (a valid immediate inference).

Worked Examples

Example 1: Statements: All pens are books. All books are red. Conclusion: All pens are red. Pens ⊂ Books ⊂ Red in every diagram → follows.

Example 2: Statements: Some cats are dogs. All dogs are animals. Conclusion: Some cats are animals. The cats that are dogs must be animals → follows.

Example 3: Statements: All A are B. Some B are C. Conclusion: Some A are C. You can draw C overlapping only the non-A part of B → conclusion can fail → does not follow.

Example 4: Statements: No table is chair. Conclusions: (I) Some tables are chairs (II) No chair is table. (I) is false; (II) is the valid reverse of "No A are B" → only II follows.

Common Mistakes

Assuming "Some A are B" implies "Some A are not B" (it does not).
Using real-world knowledge instead of the diagram (treat words as abstract sets).
Stopping at the first diagram instead of checking whether the conclusion can be broken.

Exam Tips

Always test if a conclusion can fail in some valid diagram — that is faster than proving it true.
Remember the safe inferences: Some A–B ⇒ Some B–A; All A–B ⇒ Some B–A.
For "either–or," check whether two complementary conclusions cover all diagrams.

Frequently Asked Questions

A conclusion follows only if it is true in every possible Venn diagram drawn from the statements. If you can draw even one valid diagram where the conclusion fails, it does not follow. This single rule decides every syllogism question.