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. Propositions: (a) Every student is attentive. (b) Some students are attentive. (c) Students are never attentive. (d) Some students are not attentive. Codes:
(a) and (c)
To solve the question of which propositions cannot both be true but can both be false, we need to understand the nature of the propositions provided. They belong to a category of logical statements known as categorical propositions.
- The proposition "(a) Every student is attentive" is a universal affirmative statement. It asserts that all members of the group 'students' have the attribute 'attentive'.
- The proposition "(b) Some students are attentive" is a particular affirmative statement. It claims that at least one member of the group 'students' is 'attentive'.
- The proposition "(c) Students are never attentive" is a universal negative statement. It denies that any member of the group 'students' has the attribute 'attentive'.
- The proposition "(d) Some students are not attentive" is a particular negative statement. It asserts that at least one member of the group 'students' lacks the attribute 'attentive'.
Now, we need to identify the pair of propositions where both cannot be true at the same time, yet can both be false:
- Propositions (a) and (b) can both be true simultaneously, as both indicate the presence of at least some attentive students.
- Propositions (b) and (c) cannot both be true, as (b) requires some attentiveness and (c) denies any attentiveness, but can both be false.
- Propositions (a) and (c) are directly contradictory because one asserts that every student is attentive, while the other asserts that no student is attentive. Therefore, they cannot both be true simultaneously but can be false if some students are attentive, while others aren't (satisfying proposition d).
- Propositions (c) and (d) can both be true and false, as (c) argues a universal absence of attentiveness, which could coexist with some students being inattentive as in (d).
Thus, the correct answer is the pair of propositions where both cannot be true but can both be false: (a) and (c).
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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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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(c) No domestic animal is ferocious.
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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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Code:
If proposition 'some milk is curd' is taken to be true, then which of the following propositions can be false?
When subject and predicate of both the premises is same but they differ only in quantity, it is known as:
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.
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D. Some Biologists are not outstanding teachers.
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- 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.
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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.
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C. Some sparrows are birds.
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Choose the correct answer from the options given below:
