AIEEE 2010 Solved Paper

Given that S is a non-empty subset of R.
- P : There is a rational number x∈S such that x>0.
Now, we need to find the negation of P. Clearly, P is equivalent to saying that "There is a positive rational number in S.
So, its negation (∼P) is "There is no positive rational number in S ".
Thus, for ∼P : There exists no positive rational number in S.
- ⇔∼P : Every rational number x∈S satisfies x≤0.