A. All animals are birds.
B. No birds are animals.
C. No animals are birds.
D. Some animals are birds.
Choose the correct answer from the options given below:
Reasoning with Negated Statements: Animals and Birds
The problem asks us to determine which statements are true if the given statement "Some animals are not birds" is considered false.
Understanding Statement Negation
In logic, if a statement is false, its negation must be true. The given statement is a particular negative proposition of the form "Some S are not P".
- Given Statement: "Some animals are not birds"
- This statement is False.
The negation of a "Some S are not P" statement is "All S are P".
- Therefore, the true statement is: "All animals are birds".
Analyzing the Options Based on True Statement
Now, we need to evaluate each of the proposed statements (A, B, C, D) based on the confirmed truth of "All animals are birds".
Statement A: All animals are birds.
This statement is exactly what we inferred to be true. If "All animals are birds" is true, then this statement itself is true.
Statement B: No birds are animals.
The true statement is "All animals are birds". This means the category 'animals' is entirely contained within the category 'birds'. This does not mean that the category 'birds' has no overlap with 'animals'; in fact, it implies that all animals are indeed birds. Therefore, "No birds are animals" contradicts the true statement and must be false.
Statement C: No animals are birds.
This statement is the direct opposite of "All animals are birds". If all animals are birds, then it cannot be true that no animals are birds. So, this statement is false.
Statement D: Some animals are birds.
If it is true that "All animals are birds", it logically follows that "Some animals are birds". This is because the statement "All S are P" implies that for any member of S, it is also a member of P. Thus, there exist members of S that are members of P.
Conclusion
Based on the analysis, the statements that can be inferred to be true are:
- Statement A: All animals are birds.
- Statement D: Some animals are birds.
Therefore, the correct option includes both A and D.
Important Questions from Structure of Categorical Propositions
Which of the following propositions are logically equivalent to 'No women are dishonest human beings':
(A) No dishonest human beings are women
(B) All women are non-dishonest human beings
(C) No women are non-dishonest human beings
(D) All non women are non dishonest
Choose the correct answer from the options given below:
- Which of the following propositions is logically equvalent to the proposition - "All frogs are amphibians"?
Which of the following propositions are logically equivalent?
A. No women are arrogant human beings.
B. No arrogant human beings are women.
C. All women are non-arrogant human beings.
D. All non-arrogant human beings are non-women.
Choose the correct answer from the options given below:
Which one of the following propositions is logically equivalent to the proposition-"Some attorneys are logicians"?
- Which of the following statements are logically equivalent?
A. All poems are artworks.
B. No non-poems are non-artworks.
C. Some poems are artworks.
D. All non-artworks are non-poems.
Choose the correct answer from the options given below:
