If the statement-"Some athletes are kind human beings" is given as true, then which of the following statements can be immediately inferred to be false?
No athletes are kind human beings.
This question also uses the Square of Opposition. The given true statement, "Some athletes are kind human beings", is a particular affirmative (I-type) statement.
In the square of opposition, every I-type statement has a corresponding E-type (universal negative) statement with the same subject and predicate, and these two are called CONTRADICTORIES. A key rule of contradictories is: they can never have the same truth value — if one is true, the other MUST be false, and vice versa.
The E-type statement corresponding to "Some athletes are kind human beings" is "No athletes are kind human beings" (Option 3).
Since the given I-type statement is true, its contradictory E-type statement must necessarily be false. So Option 3, "No athletes are kind human beings," is the statement that can be immediately inferred to be false.
Let's check why the other options cannot be immediately determined as false:
- Option 1, "Some athletes are not kind human beings" (O-type), is the subcontrary of the given I-type statement. When an I-type statement is true, its subcontrary can be either true or false — it is not fixed, so we cannot say it is false.
- Option 2, "All athletes are kind human beings" (A-type), is the super-altern of the given I-type statement. Truth of the I-type statement does not guarantee the truth or falsity of the A-type statement — it remains undetermined.
- Option 4, "Some kind human beings are athletes," is simply the valid simple conversion of the given true I-type statement, so it is actually TRUE, not false.
Hence, only Option 3 — No athletes are kind human beings — must be false
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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.
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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.
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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.
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:
