In a square of opposition, if 'No animals with horns are carnivores' is false, which of the following is the correct code?
codes:
A. 'Some animals with horns are carnivores' is true.
B. 'Some animals with horns are not carnivores' is true.
C. 'All animals with horns are carnivores' is false
D. 'All the animals with horns are carnivores' is undermined.
A and D Only
In the traditional square of opposition, the four standard-form propositions about a subject-predicate pair are: A (universal affirmative, 'All S are P'), E (universal negative, 'No S are P'), I (particular affirmative, 'Some S are P'), and O (particular negative, 'Some S are not P').
Here S = 'animals with horns' and P = 'carnivores', and we are told the E proposition 'No animals with horns are carnivores' is false.
E and I are contradictories: they cannot both be true and cannot both be false - exactly one of them must be true. Since E is false, its contradictory I ('Some animals with horns are carnivores') must be true. This confirms code A.
A and E are contraries: they cannot both be true, but they can both be false. Knowing only that E is false does not by itself fix the truth value of A ('All animals with horns are carnivores') - it could be true or it could be false. So the truth value of the A proposition remains logically undetermined, which confirms code D.
I and O are subcontraries: they cannot both be false, but they can both be true. Since I has already been established as true, this relation places no constraint that would make O ('Some animals with horns are not carnivores') definitely true - O's truth value is likewise left undetermined, so code B (claiming O is definitely true) is incorrect.
Code C claims the A proposition is definitely false, but as shown above the contrary relation only tells us A and E cannot both be true; it does not force A to be false whenever E is false, so code C is also incorrect.
Therefore, only codes A and D validly follow from the falsity of the E proposition, making A and D only the correct answer.
Similar Questions
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Which of the following statements are contradictory to each other?
A. All objects are perishable.
B. Some objects are not perishable.
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If the statement 'No men are honest' is given as false, then which of the following could be immediately inferred from it?
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D. 'Some men are honest' is true
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Given below are two statements
Statement I: Contrary statements are so related that if one of them is true, the other must be false.
Statement II: Contrary statements cannot both be false.
In light of the above statements, choose the correct answer from the options given below :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:
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Code:
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:
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(c) Honest people hardly suffer.
(d) Each and every honest person suffers.
Code:
Among the following propositions two are related in such a way that they cannot both be true but can both be false. Select the code that states those two propositions.
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If proposition 'some milk is curd' is taken to be true, then which of the following propositions can be false?
Important Questions from Classical Square of Opposition
Which of the following statements are so related that they can not both be true but could both be false?
A. All Biologists are outstanding teachers.
B. Some Biologists are outstanding teachers.
C. No Biologists are outstanding teachers.
D. Some Biologists are not outstanding teachers.
Choose the correct answer from the options given below:
- Which of the following propositions are so related that they can neither be true together nor can they be false together?
A. All printers are computer peripherals.
B. Some computer peripherals are printers.
C. Some printers are not computer peripherals.
D. No printers are computer peripherals.
Choose the correct answer from the options given below: - Which of the following statements contradict each other ?
A. All ducks are birds.
B. Some ducks are birds.
C. Some ducks are not birds.
D. No ducks are birds.
Choose the most appropriate answer from the options given below : - If the statement "No birds are animals" is given as false, which of the following statements can be inferred to be true ?
A. Some animals are not birds.
B. Some birds are not animals.
C. Some animals are birds.
D. Some birds are animals.
Choose the most appropriate answer from the options given below : - Which of the following statements are sub-contraries?
A. All sparrows are birds.
B. No sparrows are birds.
C. Some sparrows are birds.
D. Some sparrows are not birds.
Choose the correct answer from the options given below:
