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 a number x such that `0ltxlt1`

Explanation

To find the negation of the given statements, we will follow a systematic approach. The negation of a statement essentially means to express that the statement is not true. Let's go through each statement one by one.

### Step-by-Step Solution:

**(i) Statement p:** For every positive real number x, the number \( x - 1 \) is also positive.

**Negation of p:** There exists a positive real number x such that \( x - 1 \) is not positive.
This can be expressed as:
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