Which of the following statements are contradictory to each other? A. All objects are perishable. B. Some objects are not perishable. C. Some objects are perishable. D. No objects are perishable. Choose the most appropriate answer from the options given below:
C and D only
To determine which statements are contradictory to each other, let's analyze each given statement individually and in relation to each other:
- Statement A: All objects are perishable.
- This implies that every object, without exception, is perishable.
- Statement B: Some objects are not perishable.
- This means there is at least one object that is not perishable.
- Statement C: Some objects are perishable.
- This indicates that there is at least one object that is perishable, but not necessarily all objects.
- Statement D: No objects are perishable.
- This suggests that none of the objects are perishable.
Now, let's compare the statements to identify contradictions:
- Statement A contradicts Statement B. If all objects are perishable, then it cannot be true that some objects are not perishable.
- Statement A contradicts Statement D. If all objects are perishable, then it cannot be true that no objects are perishable.
- Statement C contradicts Statement D. If some objects are perishable, then it cannot be true that no objects are perishable.
Given the options:
- A and D only: True, they are contradictory.
- B and D only: Not contradictory. They both can coexist if some objects are perishable, but none are.
- C and D only: True, they are contradictory, as explained.
- A and C only: Not contradictory, as it is possible for all objects to be perishable, which means some are perishable by necessity.
Therefore, the statements that are most appropriately identified as contradictory are "C and D only." This is because Statement C asserts that some objects are perishable, directly opposing Statement D, which claims none are perishable.
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