8.22.b Tips, Tricks, and Shortcuts -- Syllogism

Tip 1: The Venn Diagram Method (Most Reliable)

Step-by-Step Process:

1. Read all premises carefully.
2. Identify the terms (A, B, C, etc.).
3. Draw the Venn diagram for the first premise.
4. Add the second premise to the SAME diagram.
5. If multiple valid diagrams are possible, draw ALL of them.
6. A conclusion is valid ONLY if it holds in ALL possible diagrams.
7. If a conclusion fails in even ONE diagram, it is INVALID.

Drawing Rules:

"All A are B":

  Draw A completely inside B.
  +---------+
  |    B    |
  | +-----+ |
  | |  A  | |
  | +-----+ |
  +---------+

"No A is B":

  Draw A and B completely apart.
  +-----+   +-----+
  |  A  |   |  B  |
  +-----+   +-----+

"Some A are B":

  Draw A and B overlapping.
  +----+--+----+
  | A  |XX|  B |
  +----+--+----+
  (XX = common area, at least one element exists here)

"Some A are not B":

  Draw A with part outside B.
  +------+---+----+
  | A    |XX |  B |
  +------+---+----+
  (The left part of A is outside B -- at least one element here)

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Tip 2: The "All-No" Chain Shortcut

When premises chain as All -> All -> All, or All -> No, you can directly derive:

All-All Chain:

  All A are B + All B are C  =>  All A are C
  
  A --All--> B --All--> C
  Result: A --All--> C

All-No Chain:

  All A are B + No B is C  =>  No A is C
  
  A --All--> B --No--> C
  Result: A --No--> C

Some-All Chain:

  Some A are B + All B are C  =>  Some A are C
  
  A --Some--> B --All--> C
  Result: A --Some--> C

Some-No Chain:

  Some A are B + No B is C  =>  Some A are not C
  
  A --Some--> B --No--> C
  Result: A --Some not--> C

INVALID Chains (No Conclusion):

  Some A are B + Some B are C  =>  NO definite conclusion
  All A are B + Some B are C   =>  NO definite conclusion about A and C
  Some A are not B + (anything) =>  Usually NO definite conclusion

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Tip 3: Quick Conclusion Validity Check

Shortcut Table:

For conclusions about A and C, given the relationship of A-B and B-C:

A-B	B-C	A-C Conclusion
All	All	All A are C
All	No	No A is C
All	Some	No definite conclusion
Some	All	Some A are C
Some	No	Some A are not C
Some	Some	No definite conclusion
No	All	Some C are not A (reverse only)
No	Some	No definite conclusion
Some-not	Any	No definite conclusion

Memorize the valid chains: All+All, All+No, Some+All, Some+No.

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Tip 4: The Either-Or Shortcut

When to use:

When you test two conclusions and BOTH individually fail, check if they form a complementary pair.

Complementary Pairs:

  Pair 1: "Some A are B" (I)  vs.  "No A is B" (E)
  Pair 2: "All A are B"  (A)  vs.  "Some A are not B" (O)

Quick Check:

1. Are the two conclusions about the SAME two terms (A and B)?
2. Is one of Type I and the other Type E? OR one of Type A and the other Type O?
3. If YES to both -> "Either ... or ..." follows.

Example:

  Conclusions:
  I.  Some cats are dogs.
  II. No cat is a dog.

  Both fail individually? Yes.
  Same terms (cats, dogs)? Yes.
  I is Type I, II is Type E? Yes.
  => "Either I or II follows."

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Tip 5: Handling "Possibility" Questions

Rule 1: If a conclusion is DEFINITELY true, its possibility is also true.

  If "Some A are B" definitely follows -> "Some A are B is a possibility" is also TRUE.

Rule 2: A possibility is FALSE only if it contradicts the premises.

  Premise: No A is B.
  "Is it possible that Some A are B?" -> FALSE (direct contradiction)
  "Is it possible that All A are B?"  -> FALSE (contradicts No A is B)

Rule 3: For "Some" premises, many possibilities exist.

  Premise: Some A are B.
  
  Possible: All A are B? YES (valid diagram exists)
  Possible: All B are A? YES (valid diagram exists)
  Possible: No A is B?  NO  (contradicts the premise)

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Tip 6: "Negative Conclusion" Shortcut

Rule: If one premise is negative, the conclusion (if valid) MUST be negative.

  If premises include "No X is Y":
  - Valid conclusions will be "No..." or "Some...not..."
  - "All..." or "Some...are..." conclusions are usually INVALID.

Rule: Two negative premises give NO valid conclusion.

  No A is B + No B is C  =>  NO definite conclusion about A and C.

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Tip 7: Reverse Conclusion Check

For every valid conclusion, check if its reverse is also valid:

Conclusion	Reverse	Is Reverse Valid?
All A are B	All B are A	NOT necessarily
No A is B	No B is A	YES (always valid)
Some A are B	Some B are A	YES (always valid)
Some A are not B	Some B are not A	NOT necessarily

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Tip 8: The "At Least One" Trick

In banking exams, when the answer choices include:

  (a) Only I follows
  (b) Only II follows
  (c) Either I or II follows
  (d) Neither I nor II follows
  (e) Both I and II follow

Strategy:

1. Test I independently.
2. Test II independently.
3. If both follow -> (e)
4. If only I -> (a), only II -> (b)
5. If neither follows -> check for Either-Or -> (c)
6. If neither and not complementary -> (d)

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Tip 9: Multiple Diagram Testing

When "Some" appears in premises, there are multiple valid Venn diagrams. Test ALL:

For "Some A are B" + "Some B are C":

  Diagram 1: All three partially overlap
  +---+---+---+---+
  | A | AB| BC| C |
  +---+---+---+---+

  Diagram 2: A and C overlap through B
  +---+---+---+
  | A |ABC| C |
  +---+---+---+

  Diagram 3: A and C are completely separate
  +---+--+--+---+
  | A |AB|BC| C |
  +---+--+--+---+
  (A and C don't share any region)

Since in Diagram 3, A and C are separate, "Some A are C" does NOT always hold. Since in Diagram 2, A and C overlap, "No A is C" does NOT always hold.

Result: No definite conclusion. Either-Or applies if the conclusions form a complementary pair.

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Tip 10: Avoid These Common Mistakes

Mistake 1: "All A are B" does NOT mean "All B are A"

  All cats are animals  =/=>  All animals are cats

Mistake 2: "Some A are not B" does NOT mean "Some B are not A"

  Some students are not toppers  =/=>  Some toppers are not students
  (If all toppers are students, the reverse fails!)

Mistake 3: Two particular premises give NO conclusion

  Some A are B + Some B are C  =>  NOTHING definite

Mistake 4: Two negative premises give NO conclusion

  No A is B + No B is C  =>  NOTHING definite about A and C

Mistake 5: Treating possibility as certainty

  "Some A are B" makes "All A are B" POSSIBLE but NOT CERTAIN.

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Tip 11: Speed Strategy for Exams

Step	Time	Action
1	10 sec	Read premises, identify types (A/E/I/O)
2	15 sec	Draw Venn diagram(s)
3	15 sec	Test each conclusion against diagram(s)
4	10 sec	Check for Either-Or if needed
Total	~50 sec	Per question

Time-Saving Tips:

• If premises contain "All+All" or "All+No" -- directly apply the chain shortcut.
• If both premises are "Some" -- immediately know no definite conclusion (check Either-Or).
• Practice drawing Venn diagrams fast -- use simple circles.

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