Proposition is one of the important part in Elitmus pH test, in verbal
section contains more than three questions are asked from proposition part.
Proposition is easiest one in verbal section. In this post you find more details
about Proposition and logical deduction questions and important rules for
handling those questions.
Proposition
In Logic, any
categorical statement is termed as the Proposition.
A Proposition is a
statement that asserts that either a part of, or the whole of, one set of
objects  the set identified by the subject term in the sentence expressing
that statement  either is included in, or is excluded from, another set  the
set identified by the predicate term in that sentence.
The
standard form of a proposition is:
Quantifier + Subject + Copula + Predicate
Thus, the proposition
consists of four parts:
1) Quantifier: The words 'all',
'no' and 'some' are called quantifiers because they specify a quantity 'All'
and 'no' are universal quantifiers because they refer to every object in a
certain set, while the quantifier 'some' is a particular quantifier because it
refers to at least one existing object in a certain set.
2) Subject (denoted by 'S'): The
subject is that about which something is said.
3) Predicate (denoted by 'P'):
The predicate is the part of the proposition denoting that which is affirmed or
denied about the subject.
4) Copula: The copula is that
part of the proposition which denotes the relation between the subject and the
predicate.
FourFold
Classification of Propositions:
A proposition is said
to have a universal quantity if it begins with a universal quantifier and a
particular quantity if it begins with a particular quantifier. Besides,
propositions which assert something about the inclusion of the whole or a part
of one set in the other are said to have affirmative quality, while those which
deny the inclusion of the whole or a part of one set in the other are said to
have a negative quality. Also, a term is distributed in a proposition if it
refers to all members of the set of objects denoted by that term. Otherwise, it
is said to be undistributed. Based on the above facts, propositions can be
classified into four types:
1) Universal
Affirmative Proposition (denoted by A): It distributes only the subject i.e.
the predicate is not interchangeable with the subject while maintaining the
validity of the proposition.
2) Universal Negative
Proposition (denoted by E): It distributes both the subject and the predicate
i.e. an entire class of predicate term is denied to the entire class of the
subject term, as in the proposition.
3) Particular
Affirmative Proposition (denoted by I): It distributes neither
the subject nor the predicate.
4) Particular
Negative Proposition (denoted by O): It distributes only the predicate. e.g., Some animals are not
wild. Here, the subject term 'animals' is used only for a part of its class and
hence is undistributed while the predicate term 'wild' is denied in entirety to
the subject term and hence is distributed. These facts can be summarized as
follows:
Statement
Form

Quantity

Quality

Distributed

(A):
All S is P.

Universal

Affirmative

S
only

(E):
No S is P.

Universal

Negative

Both
S and P

(I):
Some S is P.

Particular

Affirmative

Neither
S nor P

(O):
Some S is not P

Particular

Negative

P
only

Logical
Deduction:
The phenomenon of
deriving a conclusion from a single proposition or a set of given propositions,
is known as logical deduction. The given propositions are also referred to as
the premises.
Two Inferential Processes of
Deduction:
I.
Immediate Deductive Inference:
Here, conclusion is
deduced from one of the given propositions, by any of the three ways
conversion, obversion and contraposition.
1) Conversion: The
Conversion proceeds with interchanging the subject term and the predicate term
i.e. the subject term of the premise becomes the predicate term of the
conclusion and the predicate term of the premise becomes the subject of the conclusion.
The given proposition
is called converted, whereas the conclusion drawn from it is called its
converse.
Table
of Valid Conversions
Converted

Converse

A: All S is P
Ex. All pins are tops. 
I: Some P is S
Some tops are pins. 
E: No S is P.
Ex. No fish is whale. 
E: No P is S.
No whale is fish. 
I: Some S is P.
Ex. Some boys are poets. 
I: Some P is S.
Some poets are boys. 
O: Some S is not P.

No valid conversion

Note
that in a conversion, the quality remains the same and the quantity may change.
2)
Obversion: In obversion, we change the quality of the
proposition and replace the predicate term by its complement.
Table of Valid Obversions
Obverted

Obverse

A: All birds are mammals.

E: No birds are nonmammals.

E: No poets are singers.

A: All poets are nonsingers.

I: Some nurses are doctors.

O: Some nurses are not nondoctors.

O: some politicians are not
statesmen.

I: Some politicians are nonstatesmen

Contraposition: To
obtain the contra positive of a statement, we first replace the subject and
predicate terms in the proposition and then exchange both these terms with
their complements.
Table of Valid Contrapositions
Proposition

Contra positive

A: All birds are mammals.

A: All nonmammals are nonbirds.

I: Some birds are mammals.

I: Some nonmammals are nonbirds.

Note: The valid
converse, obverse or contra positive of a given proposition always logically
follows from the proposition.
II. Mediate Deductive Inference (SYLLOGISM): First introduced
by Aristotle, a Syllogism is a deductive argument in which conclusion has to be
drawn from two propositions referred to as the premises.
Example:
1. All lotus are flowers.
2. All flowers are
beautiful.
3. All lotus are beautiful.
Clearly, the
propositions 1 and 2 are the premises and the proposition 3, which follows from
the first two propositions, is called the conclusion.
Term:
In Logic, a term is a word or a combination of words, which by itself can be
used as a subject or predicate of a proposition.
Syllogism is concerned with three
terms:
1. Major Term: It is
the predicate of the conclusion and is denoted by P (first letter of
'Predicate').
2. Minor Term: It is
the subject of the conclusion and is denoted by S (first letter of 'Subject').
3. Middle Term: It is
the term common to both the premises and is denoted by M (first letter of
'Middle').