Write the negation of the statement `: p :` There exist a number x such that `0 lt x lt 1` is `"____________________"`.

Write the negation of the following statement: r: There exists a number x such that ' 0

Write negation of the statement: “There exists a complex number which is not a real Number”

Write the negation of the following statement: q: For every real number x, either x>1> or x<1

0 lt |x-1|lt3

Show that the statement : "Given a positive number x, there exists a rational number r such that 0 lt r lt x is true.

Write the negation of each of the following : x gt 3 or x lt 3 .

Write the negation of the following statements: (i) p : For every positive real number x, the number x" "-" "1 is also positive. (ii) q : All cats scratch. (iii) r : For every real number x, either x" ">" "1 or x" "<" "1 . (iv) s : There exist

Write the negation of the following statement: p: For every positive real number x, the number (x-1) is also positive.

The negation of the statement p : ''For every positive real number x, the number x - 1 is also positive'' is

For any positive real number x , prove that there exists an irrational number y such that 0 lt y lt x .