Master this topic with zero to advance depth.
Syllogism deductions rely on 4 standard propositions:
тАв A (All): Universal Positive (e.g., All A are B).
тАв E (No): Universal Negative (e.g., No A is B).
тАв I (Some): Particular Positive (e.g., Some A are B).
тАв O (Some...Not): Particular Negative (e.g., Some A are not B).
When using Venn Diagrams, always draw the Minimum Overlapping Diagram. A conclusion is 'Definite' only if it holds true in ALL possible diagrams.
Standard Conversions:
тАв All A are B converts to Some B are A.
тАв No A is B converts to No B is A and Some B are not A.
тАв Some A are B converts to Some B are A.
тАв Some A are not B CANNOT be strictly converted.
For speed, assign values to Subject and Predicate:
тАв A (All): Sub=100, Pred=50 (+)
тАв E (No): Sub=100, Pred=100 (-)
тАв I (Some): Sub=50, Pred=50 (+)
тАв O (Some..Not): Sub=50, Pred=100 (-)
Rules:
1. Positive statements give Positive conclusions. Negative gives Negative.
2. If linking two statements, the common term MUST have at least one 100.
3. Value Check: A value of 50 in the statement cannot become 100 in the conclusion (You can't spend 100 if you only earn 50).
тАв Only A is B: Means 'All B is A' AND B cannot overlap with anything else. Think of B as a restricted entity.
тАв Only a few A are B: This means 'Some A are B' AND 'Some A are NOT B'. It is a combination statement. Conclusion 'All A are B is a possibility' is strictly FALSE. But 'All B are A is a possibility' is TRUE.
Either/Or Conditions:
1. Both conclusions must be individually false (doubtful).
2. Subjects and Predicates must be exactly the same.
3. They must form a complementary pair: (Some + No) or (All + Some...Not) or (Some + Some...Not).
Possibility: If the relation between two elements is 'unknown' or 'doubtful', ANY possibility between them is TRUE.