This document discusses the square of opposition, which is a logical diagram that shows the relationships between categorical propositions. It defines the types of relationships between propositions as contradictory, contrary, sub-contrary, and sub-altern. It then provides examples of how to determine which propositions can be true or false based on these relationship types.

1. SQUARE OF
OPPOSITION
Siva Prasath T R
UGC Junior Research Fellow
Department of Social Work
Pondicherry Central University
sivaprasathtr@gmail.com
Ph:9500436023
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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2. AFFIRMATIVE NEGATIVE
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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3. UNIVERSAL
PARTICULAR
A E
I O
Contradictory
Contrary
Sub-Contrary
Sub-altern Sub-altern
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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4. •Contradictory
A→ O
O→ A
I→ E
E→ I
Both cannot be true
Both cannot be false
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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5. •Contrary
Both cannot be true
Both can be false
A is true then E should be false
If A is false then E can be true or
false
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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6. •Sub-Contrary
Both can be true
Both cannot be false
If I is true then O can be true or
false
I is false then O should be true
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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7. •Sub-altern
Both true together
Both false together
If Universal is true then particular
should be true
If Universal is false then particular
can be true/false
If particular is false then Universal
should be false
If particular is true then Universal
can be true/false
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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8. If proposition ‘All republics are grateful’ is taken to be true then which of the following
propositions can be false?
(i) Republics are not grateful
(ii) Some republics are not grateful
(iii) No republics are grateful
(iv) Some republics are grateful
Select the correct answer from the options given below:
(1) (i) only
(2) (ii) only
(3) (i). (ii) and (iii)
(4) (ii) and (iii)
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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9. Among the following, there are two statements which can’t be true together, but can be false
together. Select the code that represents them.
Statements:
(a) All poets are dreamers.
(b) No poets are dreamers.
(c) Some poets are dreamers.
(d) Some poets are not dreamers.
1. (a) and (b)
2. (b) and (d)
3. (a) and (d)
4. (c) and (d)
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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10. If the proposition ‘domestic animals are hardly ferocious’ is taken to be false, which of the following
proposition/propositions can be claimed to be certainly true? Select the correct code:
Propositions:
(a) All domestic animals are ferocious.
(b) Most of the domestic animals are ferocious.
(c) No domestic animal is ferocious.
(d) Some domestic animals are non-ferocious.
Code:
(1) (a) and (b)
(2) (a) only
(3) (c) and (d)
(4) (b) only
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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11. Given below are four statements. Among them, two are related in such a way that they can both be
true but they cannot both be false. Select the code that indicates those two statements:
Statements:
(a) Honest people never suffer.
(b) Almost all honest people do suffer.
(c) Honest people hardly suffer.
(d) Each and every honest person suffers.
Code:
(1) (a) and (c)
(2) (a) and (d)
(3) (b) and (c)
(4) (a) and (b)
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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12. If the statement 'None but the brave wins the race' is false which of the following statements can
be claimed to be true?
Select the correct code:
(1) All brave persons win the race.
(2) Some persons who win the race are not brave.
(3) Some persons who win the race are brave.
(4) No person who wins the race is brave.
Siva Prasath T R (UGC Junior Research Fellow)
Department of Social Work , Pondicherry Central University
sivaprasathtr@gmail.com , 9500436023
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