I am Akshay Sharma.
Here I am sharing some Syllogism Shortcut Rules. Hope it will help all aspirants. Happy Reading :)
Type of proposition
Type of inference(convertible to)
All S are P
Some S are
P,some P are S
No S is P
Some S are not P,No P is S.
Some S are P
Some P are S
Some S are not P
Here S-subject, P-predicate. inferences are done to make statements conclusive
e.g. some s are p + all s are q ,then we have to convert 1st statement in this case to make both statements conclusive
some p are s+ all s are q= some p are q
we convert or create inference statement , in priority order first convert I then E then A.if all the three are given in statements.if not then which is given .
1st statement + 2nd statement = conclusion
A + E = E
E + A= O*
E + I = O*
I + A = I
I + E = O
A + I = NO RESULT
O* = predicate of second + subject of first
e.g. No s is p + some p are r = some r are not s
I-O, A-O, I-E = either cases or complamentary case , in conclusion if any conclusion is not followed and a complamentry pair is there then either I or O follows if these complamentry pairs are given in conclusion.but both should have same subject and predicate
Possibility case- in conclusion if we have;
Some S are not P ↔ All P are S is a possibility. These are reconvertible
Some S are P – All S are P is a possibility
NO conclusion – any possibility
Here conclusion means that which we get after applying above rules.these conclusions may or not be provided.in case of three statement problem ,we have to first solve two statement then its conclusion + 3rd statement
e.g No home is an office,all offices are houses,some houses are huts
conclusion given-all homes being houses is a possibility
solution- 1st statement+ 2nd statement , E+A= O* = some houses are not homes, now convert it into possibility – all home being houses in a possibility.
There are two types of method .venn and rules method.i follow rules method.many may use venn diagram .it upto our comfortabality with respective method.we have to practice to be comfortable.
If any query or suggestion regarding this method ,you can mail me at - firstname.lastname@example.org.
Sources – arihant book on reasoning and internet.