Let S be a non-empty subset of R. Consider the following statement:
P : There is a rational number x ∈ S such that x > 0.
Which of the following statements is the negation of the statement P?

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

Consider the following relations

$R=\{(x, y) \mid x, y$ are real numbers and $x=w y$ for some rational number $w\}$;

$S=\left\{\left(\frac{m}{n}, \frac{p}{q}\right) \mid m, n, p\right.$ and $q$ are integers such that $n, q \neq 0$ and $q m=p m\}$. Then

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $$ \times $$ 10^–3 are