Question
Download Solution PDFWhich of the following propostions are so related that they cannot both be false, although they may both be true?
A. All cricketers are cheerful persons.
B. No cricketers are cheerful persons.
C. Some cricketers are not cheerful persons.
D. Some cricketers are cheerful persons.
Choose the correct answer from the options given below:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF- Propositions A and B are contraries. This means that they cannot both be true, but they can both be false. For example, it is possible that some cricketers are cheerful persons, but not all cricketers are cheerful persons.
- Propositions C and D are subcontraries. This means that they cannot both be false, although they may both be true. For example, it is possible that some cricketers are not cheerful persons, but it is also possible that some cricketers are cheerful persons.
- Proposition A cannot be true if proposition C is true, and proposition B cannot be true if proposition D is true. However, it is possible for both propositions C and D to be true at the same time. For example, if there are 100 cricketers, and 50 of them are cheerful persons, then proposition C is true, and proposition D is also true.
Therefore, the only propositions that cannot both be false are C and D.
Last updated on Jun 12, 2025
-> The UGC NET June 2025 exam will be conducted from 25th to 29th June 2025.
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