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@Partho your answer is correct. None of the options follow.
Option 2 and 4 are the same exact statement, since all balls can either be white or black. Therefore, all balls are white implies that no balls are black. Hence, since they are the same statement they can either both be true or both be false.
The questions asks for statements that can both be true, but cannot both be false. No two such statements are mentioned.
Ah Damn! True, 2 & 4 are synonyms, so can be false together.
But still not convinced with the way partho was going about the question.
@Partho your answer is correct. None of the options follow.
Option 2 and 4 are the same exact statement, since all balls can either be white or black. Therefore, all balls are white implies that no balls are black. Hence, since they are the same statement they can either both be true or both be false.
The questions asks for statements that can both be true, but cannot both be false. No two such statements are mentioned.
Ah Damn! True, 2 & 4 are synonyms, so can be false together.
But still not convinced with the way partho was going about the question.
@Partho 's logic is intact but I can understand why it looks confusing. Everyone has their own way of understanding and analysing. Though a question like this should not take >15 secs to answer.
Just googled the question @Sourabh16 asked. Seems like they've asked this question in UPSC prelims 1997. In the book,its given a combination of 'Only some balls are black' and 'No balls are black' is the right answer. Here is the link
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But still not convinced with the way partho was going about the question.
"My motto in life is: If anything is worth doing then it is worth over doing."
I was also thinking that none would be correct, but the answer given in book was D
2 and 4 is correct.
I'll remember that.
In the book,its given a combination of 'Only some balls are black' and 'No balls are black' is the right answer.
Here is the link