⭐ Sabse Important Points · एक नज़र में
- Universal Affirmative (A): All S are P – S is entirely within P; conclusion 'Some P are S' is not necessarily true unless existence is implied.
- Rule of Particular: If both premises are particular (I or O), no conclusion follows.
- Universal Negative (E): No S are P – S and P are disjoint; conclusion 'No P are S' is always true.
- Rule of Negative: If both premises are negative (E or O), no conclusion follows.
- Particular Affirmative (I): Some S are P – at least one S is also P; conclusion 'Some P are S' is always true.
- Distribution: In 'All S are P', S is distributed; in 'No S are P', both S and P are distributed; in 'Some S are P', neither is distributed; in 'Some S are not P', P is distributed.
Introduction · परिचय
Syllogism is a logical reasoning topic where conclusions are drawn from given statements (premises) using the rules of categorical propositions. In LIC AAO, questions typically present two or more statements and ask which conclusions logically follow. Mastery of Venn diagrams and standard rules is essential for quick and accurate solving.
Basics of Categorical Propositions and Venn Diagrams
A categorical proposition relates two terms (subject and predicate) using quantifiers: All, No, Some, Some not. The four standard forms are A (All S are P), E (No S are P), I (Some S are P), O (Some S are not P). Venn diagrams visually represent these relationships and help test conclusions. For 'All S are P', S is inside P; for 'No S are P', S and P are disjoint; for 'Some S are P', there is at least one common element; for 'Some S are not P', there is at least one S outside P.
- Read statements
- Identify proposition types (A/E/I/O)
- Draw minimal Venn diagram
- Check each conclusion against all possible diagrams
- Mark follows/does not follow
⭐ Key Points · याद रखने वाली बातें
- Universal Affirmative (A): All S are P – S is entirely within P; conclusion 'Some P are S' is not necessarily true unless existence is implied.
- Universal Negative (E): No S are P – S and P are disjoint; conclusion 'No P are S' is always true.
- Particular Affirmative (I): Some S are P – at least one S is also P; conclusion 'Some P are S' is always true.
- Particular Negative (O): Some S are not P – at least one S is outside P; no direct conversion to 'Some P are not S'.
✍️ Solved Example 1 · हल किया हुआ उदाहरण
❓ Question: Statements: All cats are dogs. Some dogs are birds. Conclusions: I. Some cats are birds. II. Some birds are dogs.
✅ Solution: Only II follows.
💡 Explanation: Draw Venn: Cats inside Dogs; Dogs overlap Birds. Conclusion I: Cats and Birds may or may not overlap, so not definite. Conclusion II: Since some dogs are birds, some birds are dogs (conversion of I) is always true.
Rules for Combining Statements and Checking Conclusions
When multiple statements share a common term, combine them to form a conclusion. Key rules: (1) Two particulars give no conclusion. (2) Two negatives give no conclusion. (3) If one premise is particular, conclusion must be particular. (4) If one premise is negative, conclusion must be negative. (5) The middle term must be distributed at least once. Also, for 'possibility' conclusions, check if the conclusion can be true in any valid Venn diagram; if yes, it is a possibility.
📐 Formula / Rule Box · सूत्र याद रखो
Conversion
All S are P → Some P are S (not always); No S are P → No P are S; Some S are P → Some P are S
Distribution
A: S distributed; E: S and P distributed; I: none; O: P distributed
Rule of Particular
If both premises are particular (I or O), no conclusion follows.
Rule of Negative
If both premises are negative (E or O), no conclusion follows.
| Conclusion Type | When it follows |
|---|---|
| Definite | True in all possible Venn diagrams |
| Possibility | True in at least one valid Venn diagram |
| Does not follow | False in at least one valid Venn diagram |
⭐ Key Points · याद रखने वाली बातें
- Distribution: In 'All S are P', S is distributed; in 'No S are P', both S and P are distributed; in 'Some S are P', neither is distributed; in 'Some S are not P', P is distributed.
- Possibility: A conclusion is a possibility if it is true in at least one valid Venn diagram; it is definite only if true in all valid diagrams.
✍️ Solved Example 1 · हल किया हुआ उदाहरण
❓ Question: Statements: All pens are books. No book is a pencil. Conclusions: I. No pen is a pencil. II. Some pencils are pens.
✅ Solution: Only I follows.
💡 Explanation: Pens inside Books; Books disjoint from Pencils. So Pens disjoint from Pencils → I true. II contradicts I, so false.
Practice Questions · खुद हल करके देखो
पहले खुद try karo, phir “Answer dekho” dabakar check karo. 👇
Q1Statements: Some roses are flowers. All flowers are plants. Conclusions: I. Some roses are plants. II. All plants are roses.
👀 Answer dekho
✅ Answer: Only I follows.
💡 Explanation: Roses overlap Flowers; Flowers inside Plants → Some roses are plants (I). II is not necessarily true because Plants may include other things.
Q2Statements: No teacher is a doctor. Some doctors are engineers. Conclusions: I. Some engineers are not teachers. II. No engineer is a teacher.
👀 Answer dekho
✅ Answer: Only I follows.
💡 Explanation: Doctors disjoint from Teachers; Some Doctors are Engineers → Those engineers are doctors, so they are not teachers → I true. II is not definite because some engineers may be teachers (not ruled out).
Q3Statements: All cars are vehicles. Some vehicles are electric. Conclusions: I. Some cars are electric. II. Some electric are vehicles.
👀 Answer dekho
✅ Answer: Only II follows.
💡 Explanation: Cars inside Vehicles; Vehicles overlap Electric. I: Cars and Electric may or may not overlap → not definite. II: Conversion of 'Some vehicles are electric' → Some electric are vehicles → true.
⚠️ Common Mistakes · ये गलतियाँ बिल्कुल मत करना
- Assuming 'All S are P' implies 'All P are S' – avoid by checking converse only if existence is given or for particular statements.
- Ignoring the possibility case: marking a conclusion as 'does not follow' when it is a possibility – always consider all valid Venn diagrams.
- Combining two particular statements to draw a conclusion – remember the rule that two particulars yield no conclusion.
⚡ Quick Revision · Exam से पहले 2 मिनट में दोहराओ
- Proposition Types: A (All), E (No), I (Some), O (Some not) – know their Venn representations and conversions.
- Combination Rules: Two particulars → no conclusion; two negatives → no conclusion; one particular → particular conclusion; one negative → negative conclusion.
- Possibility Check: A conclusion is a possibility if it holds in at least one valid Venn diagram; definite only if holds in all.