Logical Reasoning is an important and unique section of UGC NET Paper 1 syllabus. Structure of argument, syllogism, Analogies, Indian logics and Deductive and Inductive Reasoning are few topics that constitute the unit of Logical Reasoning. We are trying to cover all these topics to help you prepare for your examination. Now, let's sharpen your understanding of the topic of Square of Opposition.
The square of opposition is a diagram that explains the relation and the bond between the four categorical propositions (A, E, I, O).
Each corner of the figure represents four types of Proposition.
A- Type propositions also called universal affirmatives are in the form: All S are P.
E- Type propositions, also called universal negations are in the form: No S are P.
I- Type propositions also called particular affirmatives are in the form: Some S are P.
O- Type propositions also called particular negations are in the form: Some S are not P.
There are four types of Squares of opposition-
A contradiction is a relationship between two propositions which cannot be both true and cannot be both false. A and E, I and O propositions are contradictory to each other. Here we see that the truth of a proposition of the form All S are P implies the falsity of the corresponding proposition of the form Some S are not P.
For example, if the proposition “all entrepreneur are capitalists” is true, then the proposition “some entrepreneur are not capitalists” must be false.
Consider the proposition “person who professes atheism yet goes to church every Sunday. Here both be cannot be true and also both cannot be false.
Contrary is the relationship between two propositions when they cannot be both true but both can be false. A and E propositions are contrary.
For example, an A proposition “all giraffes have long tails” cannot be true at the same time as the corresponding E proposition: “no giraffes have long tails.”Also since both of them cannot be false, they cannot be Contradictory. For instance, “all planets are gas giants” and “no planets are gas giants.”
Sub contrary is the relationship between two propositions which cannot be both false, but both can be true. Here, I and O propositions are contrary. For example, consider two statements-There exist some mango that is delicious. There exists some mango that is not delicious. This example is ideal examples of sub contrary- both can be true but both cannot be false since there are chances of some being delicious and some being not delicious.
Subaltern is the relationship between two propositions which cannot be pairs can both be true or both be false. A propositions and I propositions have a sub alternation relation between them.
The truth of the A proposition “all plastics are synthetic,” implies the truth of the proposition “some plastics are synthetic.” However, the truth of the O proposition “some cars are not Japan-made products” does not imply the truth of the E proposition “no cars are Japan-made products.” The truth of an A or E proposition implies the truth of the corresponding I or O proposition, respectively. Consequently, the falsity of I or O proposition implies the falsity of the corresponding A or E proposition, respectively.
Practice Questions :
Q1. Which one of the following propositions is a contrary to “All dancers are talented”?
a) No dancers are talented.
b) Some dancers are not talented.
c) Some dancers are talented.
d) No talented persons are dancers.
Ans- a)Contrary propositions are those which they cannot both be true but both may be false. So in this case, Contrary to “all dancers are talented” is “no dancers are talented”.
Q2. Sub-contrary to the preposition “Some cats are apples” is?
a) No cats are apples
b) Some cats are not apples
c) All cats are apples
d) Some cats are apples.
Ans- b) Sub contrary is the relationship between two propositions which cannot be both false, but both can be true. In this case sub contrary to the proposition “some cats are apples” is “some cats are not apples”.
Q3. If the statement ‘all girls are intelligent’ is true, which of the following statements are false?
- No girls are intelligent.
- Some girls are intelligent.
- Some girls are not intelligent.
Choose the correct option:
A. 1 and 2
B. 2 and 3
C. 1 and 3
D. 1 only
Ans- c) The statement all girls are intelligent are universal positive proposition. If the universal positive is true, then particular negative will be false due to the contrary relationship. Thus contrary of this statement is ‘some girls are not intelligent’. Also in a contrary relationship, if the universal positive is true, then universal negative i.e. ‘No girls are intelligent’ is false.
Q4. If the proposition “all policemen are poor is false”, which the following proposition can be claimed to be true?
A. Some policemen are poor
B. Some policemen are not poor
C. No policemen is poor
D. No poor person is a policeman.
Ans-b) Here we cannot be sure of the reason for the statement "All policemen are poor" to be considered false. Since all policemen are poor is false given as false, proposition such as “some policemen are poor”, “no policemen is poor”, “no poor person is a policemen” can be considered as false But one thing is sure if "all policemen are poor" is false, then there must be some policemen who are not poor.
Hope you all now have a better understanding of Square of Opposition. If you have any other questions, please comment.
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