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.
Four-Fold 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 non-mammals.
|
E: No poets are singers.
|
A: All poets are non-singers.
|
I: Some nurses are doctors.
|
O: Some nurses are not non-doctors.
|
O: some politicians are not statesmen.
|
I: Some politicians are non-statesmen
|
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 non-mammals are non-birds.
|
I: Some birds are mammals.
|
I: Some non-mammals are non-birds.
|
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').
For example, try reading these numbers:
7516324 This is hard to read and remember.
751-6324 This is easier because of chunking.
123-4567 This is easy to read because of prior knowledge and structure.
Similarly, if you like sports, then reading the sports page is easy. You have a framework in your mind for reading, understanding and storing information.
Improving Comprehension.
Reading comprehension requires motivation, mental frameworks for holding ideas, concentration.
Develop a broad background.
Broaden your background knowledge by reading newspapers, magazines and books. Become interested in world events
Does the author use cause and effect reasoning, hypothesis, model building, induction or deduction, systems thinking.
Anticipate and predict.
Really smart readers try to anticipate the author and predict future ideas and questions. If you're right, this reinforces your understanding. If you're wrong, you make adjustments quicker.
Create motivation and interest.
Preview material, ask questions, discuss ideas with classmates. The stronger your interest, the greater your comprehension.
Pay attention to supporting cues.
Study pictures, graphs and headings. Read the first and last paragraph in a chapter, or the first sentence in each section.
Know the structure of paragraphs.
Good writers construct paragraphs that have a beginning, middle and end. Often, the first sentence will give an overview that helps provide a framework for adding details. Also, look for transitional words, phrases or paragraphs that change the topic.
Highlight, summarize and review.
Just reading a book once is not enough. To develop a deeper understanding, you have to highlight, summarize and review important ideas.
Build a good vocabulary.
For most educated people, this is a lifetime project. The best way to improve your vocabulary is to use a dictionary regularly.
Use a systematic reading technique like SQR3.
Develop a systematic reading style, like the SQR3 method and make adjustments to it, depending on priorities and purpose. The SQR3 steps include Survey, Question, Read, Recite and Review.
Example: Crestfallen by having done poorly on the GRE, Susan began to question her abilities. Her self-confidence was ..........
A.appeased
B. destroyed
C. placated
D. elevated
E. sustained
If somebody is crestfallen (despairing) and has begun to question herself, then her self-confidence would be destroyed. Hence, the answer is (B).
Transitional Words:
Be alert to transitional words. Transitional words tell you what is coming up. They indicate that the author is now going to draw a contrast with something stated previously, or support something stated previously.
i. Contrast Indicators:
To contrast two things is to point out how they differ. In this type of sentence completion problem, we look for a word that has the opposite meaning (an antonym) of some key word or phrase in the sentence.
Following are some of the most common contrast indicators:
But
Yet
Despite
Although
However
Nevertheless
Following are some of the most common contrast indicators:
But
Yet
Despite
Although
However
Nevertheless
Example: Although the warring parties had settled a number of disputes, past experience made them .......... to express optimism that the talks would be a success.
A. rash
B. ambivalent
C. scornful
D. overjoyed
E. reticent
"Although" sets up a contrast between what has occurred--success on some issues--and what can be expected to occur--success for the whole talks. Hence, the parties are reluctant to express optimism. The common word "reluctant" is not offered as an answer-choice, but a synonym--reticent--is. The answer is (E).
A. rash
B. ambivalent
C. scornful
D. overjoyed
E. reticent
"Although" sets up a contrast between what has occurred--success on some issues--and what can be expected to occur--success for the whole talks. Hence, the parties are reluctant to express optimism. The common word "reluctant" is not offered as an answer-choice, but a synonym--reticent--is. The answer is (E).
ii. Support Indicators:
Supporting words support or further explain what has already been said. These words often introduce synonyms for words elsewhere in the sentence.
Following are some common supporting words:
And
Also
Furthermore
Likewise
In Addition
For
Following are some common supporting words:
And
Also
Furthermore
Likewise
In Addition
For
Example: Davis is an opprobrious and .......... speaker, equally caustic toward friend or foe--a true curmudgeon.
A.lofty
B. vituperative
C. unstinting
D. retiring
E. laudatory
"And" in the sentence indicates that the missing adjective is similar in meaning to "opprobrious," which is very negative. Now, vituperative--the only negative word--means "abusive." Hence, the answer is (B).
A.lofty
B. vituperative
C. unstinting
D. retiring
E. laudatory
"And" in the sentence indicates that the missing adjective is similar in meaning to "opprobrious," which is very negative. Now, vituperative--the only negative word--means "abusive." Hence, the answer is (B).
iii. Cause And Effect Indicators:
These words indicate that one thing causes another to occur.
Some of the most common cause and effect indicators are
Because
For
Thus
Hence
Therefore
If , Then .
Some of the most common cause and effect indicators are
Because
For
Thus
Hence
Therefore
If , Then .
Example: Because the House has the votes to override a presidential veto, the President has no choice but to ..........
A. object
B. abdicate
C. abstain
D. capitulate
E. compromise
Since the House has the votes to pass the bill or motion, the President would be wise to compromise and make the best of the situation. The answer is (E).
A. object
B. abdicate
C. abstain
D. capitulate
E. compromise
Since the House has the votes to pass the bill or motion, the President would be wise to compromise and make the best of the situation. The answer is (E).
Apposition:
This rather advanced grammatical structure is very common on the GRE. (Don't confuse "apposition" with "opposition": they have opposite meanings.)
Words or phrases in apposition are placed next to each other, and the second word or phrase defines, clarifies, or gives evidence to the first word or phrase.
The second word or phrase will be set off from the first by a comma, semicolon, hyphen, or parentheses.
Note: If a comma is not followed by a linking word--such as and, for, yet--then the following phrase is probably appositional.
Identifying an appositional structure, can greatly simplify a sentence completion problem since the appositional word, phrase, or clause will define the missing word.
Words or phrases in apposition are placed next to each other, and the second word or phrase defines, clarifies, or gives evidence to the first word or phrase.
The second word or phrase will be set off from the first by a comma, semicolon, hyphen, or parentheses.
Note: If a comma is not followed by a linking word--such as and, for, yet--then the following phrase is probably appositional.
Identifying an appositional structure, can greatly simplify a sentence completion problem since the appositional word, phrase, or clause will define the missing word.
Example: His novels are .......... ; he uses a long circumlocution when a direct coupling of a simple subject and verb would be best.
A. prolix
B. pedestrian
C. succinct
D. vapid
E. risque
The sentence has no linking words (such as because, although, etc.). Hence, the phrase following the semicolon is in apposition to the missing word--it defines or further clarifies the missing word. Now, writing filled with circumlocutions is aptly described as prolix. The answer is (A).
A. prolix
B. pedestrian
C. succinct
D. vapid
E. risque
The sentence has no linking words (such as because, although, etc.). Hence, the phrase following the semicolon is in apposition to the missing word--it defines or further clarifies the missing word. Now, writing filled with circumlocutions is aptly described as prolix. The answer is (A).
Punctuation:
Whenever the punctuation "," (comma) appears, followed by a blank in between two sentences, then it means that the synonym of the phrase/word before "," is the meaning of the blank. In simple words, when you find ',' followed by a blank then find the synonym of the word before ',' and check the options to match the synonym of the word.
In the same way, when you find ":"( colon) or ";"( semi-colon) in the sentence, they will indicate that the idea coming up is merely an explanation of the earlier idea. So, simply find the synonym of the word/phrase before the punctuation and fill in the blank with the synonym from the options given.
Positive/Negative Flow:
When you read the sentence, you have to look out for adjectives/adverbs which tell you the idea of the sentence. After finding these adjectives/adverbs, you need to find out if the idea of the sentence is positive/negative. All the negative ideas may be a "bad word/bad phrase" or any term which has no/none/not... in it.
You need to just go on marking the words with +/- and keep on doing till the end of the sentence. Then you need to use the punctuations/conjunctions clue which would break the sentence into 2/3 parts. After that you need to compare the +/- signs on both sides and enter the desired sign in the blank. In simple words, if the flow of the first part of the sentence is positive and the second part is negative, then the blank must be negative to even the flow of the sentence. This would solve the sentence completion question without even understanding the question.
Example: Because he did not want to appear_______, the junior executive refused to dispute the board's decision, in spite of his belief that the decision would impair employee morale.
A. contentious
B. indecisive
C. solicitous
D. overzealous
E. steadfast
B. indecisive
C. solicitous
D. overzealous
E. steadfast
Explanation: (C) and (E) are gone because they're positive words. .(B)doesn't work because the clue is "refused to dispute." That doesn't work with indecisive. For the same reason,(D) doesn't work either. So the best answer is option A.
Process of Elimination(POE):
You can easily eliminate all the options that are definitely wrong or are eliminated through the positive/negative flow. Suppose if you have a blank in the sentence for which the answer is positive, then you can eliminate all the options which are negative. In this way you can eliminate options and have very less options remaining. The probability of you getting right answer from 2 options is much higher than you getting right from 5 options.
