SYLLOGISM : POSSIBILITIES

                                                           

                                     SYLLOGISM :  POSSIBILITIES
                                     


                      Questions based on possibilities are often asked in various


competitive exams. To solve syllogism questions on
possibilities, following points should be kept in mind:
(1) When definite conclusions (either definitely true or
definitely false) can be drawn from the given
propositions, they are certainties. It is to be noted
that conclusions can be drawn either by ‘immediate
inference’ (implication or conversion) or by ‘mediate
inference’ (combining pair of aligned propositions).
For example, take an A-type proposition as given
below:

All S are P
For this statement, following are the definite
conclusions:
(i) All S are P  conversion  Some P are S
[Definitely True]
[Since, on conversion of A-Type statement, we
obtain I-type of statement]
(ii) All S are P  implication  Some S are P
[Definitely True]
(iii) No S are P [Definitely False]
(iv) Some S are not P [Definitely False]
Therefore, the above drawn conclusions are cases of
certainties.
(2) When definite conclusions cannot be drawn from the
pair of aligned statements (mediate inference), cases
of possibilities exist.
It should be noted that there are only six cases where
a conclusion can be drawn. These cases are as given
below:
A + A = A
A + E = E
E + A = O*
E + I = O*
I + A = I
I + E = O
Except the abovementioned cases, in all other cases,
possibilities exist.
A + I = –
A + O = –
E + E = –
E + O = –
I + I = –
I + O = –
O + [A or E or I or O] = –
Note: ‘–’ stands for ‘No conclusion’.
Now, we analyse the different cases of possibilities in
the following pages:
Immediate Possibilities
A-Type [All S are P]
I. Implication
Conclusions:
(i) Some S are P [True]
(ii) Some S are not P [False]
(iii) No S are P [False]
The above three conclusions are either definitely true
or definitely false.
II. Conversion
We know that A-Type of statements can be converted
to I-Type of statements. Therefore, All S are P 
conversion  Some P are S
Hence, ‘Some P are S’ is a definite conclusion.
But ‘All P are S’ is a possibility.
E-Type [No S are P]
I. Implication
Conclusions:
(i) All S are P [False]
(ii) Some S are P [False]
(iii) Some S are not P [True]
The above conclusions are either definitely true or
definitely false.
II. Conversion
No S are P(E)  conversion  No P are S (E).
Therefore, ‘No P are S’ is a case of certainty.
I-Type [Some S are P]
I. Implication
Conclusions:
(i) No S are P [False]
The above conclusion is definitely false.
Cases of Possibilities:
(i) All S are P [Doubtful]
(ii) Some S are not P [Doubtful]
All the above statements are cases of possibilities.
II. Conversion
Some S are P (I)  conversion  Some P are S (I). The
above statement is a definite conclusion obtained by
conversion of the given I-Type of proposition. There
are some possibilities related to I-type of statements
as given below:
(i) All P are S
(ii) Some P are not S