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`.

Explanation

To find the negation of the given statements, we will follow a systematic approach. The negation of a statement essentially means stating that the original statement is not true.

### Step-by-Step Solution:

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

**Negation:** The negation of this statement would be:
"There exists a positive real number \( x \) such that \( x - 1 \) is not positive."
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