General Trick for Solving all Syllogism Possibility Problem: Explained with an UPSC Question (Asked as Youtube Comment) [ IAS Updates ]

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This post is in response to a slightly tricky syllogism question mentioned as youtube comment on this video, the types of which have been asked recently in several competitive examinations. Here the conclusion deviate from the normal. Let us consider one such problem: Statements: Some teachers are professors. Some lecturers are teachers.

Conclusion I: All teachers as well as professors being lecturers is a possibility.

Conclusion II: All those teachers who are lecturers are also professors.

Solution: The venn diagram for this problem can be drawn as follows:

Venn Diagram depicting, professors, lecturers and teachers

Venn Diagram depicting, professors, lecturers and teachers

X signs denotes some.

Note that both the premises result in an “X” which is shared between two regions (4 and 7; 5 and 7 respectively). This means that item can exist either region or both regions. Now lets look at the conclusion one by one.

Conclusion I: All teachers as well as professors being lecturers is a possibility.

This is a non standard conclusion and it asks us the “POSSIBILITY”- the possibility of all teachers as well as professors being lecturers. If we move both the “X’s” to region 7 (which is ofcourse a possibility) based on the premises then this conclusion stands true. In other words, the premises do not preclude the possibility of all teachers as well as professors being lecturers.

Conclusion II: All those teachers who are lecturers are also professors.

This conclusion is invalid since the “X” between region 5 and 7 can go to region 5 and make the region 7 empty.

You can watch several more examples in this video - Syllogism Problems Solved Step by Step

For reference:

Unconditionally valid forms of syllogism cases:

Unconditionally valid forms of syllogism cases

Unconditionally valid forms of syllogism cases

Figure 1

Figure 2

Figure 3

Figure 4

AAA

EAE

IAI

AEE

EAE

AEE

AII

IAI

AII

EIO

OAO

EIO

EIO

AOO

EIO

Conditionally valid forms of syllogism cases:

Conditionally valid forms of syllogism cases

Conditionally valid forms of syllogism cases

Figure 1

Figure 2

Figure 3

Figure 4

Required Condition

AAI, EAO

AEO, EAO

-

AEO

S exists

-

-

AAI, EAO

EAO

M exists

-

-

-

AAI

P Exists

If you observe closely, the two premises and conclusion 2 are of IIA form which is not valid in any of the figures.

- Published on: August 20, 2015