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

        p = {(x-1) > 0 | ∀x ∈ R⁺ }

(ii) q: All cats scratch

          q = {x scratchs | ∀x ∈ cat }}

(iii) r: For every real number x, either x > 1 or x < 1

          p = {x> 1 or x<1 | ∀x ∈ R }

(iv) s: There exists a number x such that 0 < x < 1

         p = {0< x< 1 | ∃x ∈ R }