Write the negation of the following stat...

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

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(i) there exists a positive real number x such that `x-1` is not positive.
(ii) there exists at least one cat which does not scratch.
(iii) there exists a real number `x` such that neither `xgt1` nor `xlt1`.
(iv) For every real number `x,x le0`or `xge1`.

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

there exists atleast one positive real number x for which (x -1) is not positive

for every positive real number x, the number (x +1) is also positive

Both (a) and (b)

Neither (a) nor (b)

If x and y are positive real number, then :

`x gt y implies -x gt -y`

`x gt y implies -x lt - y`

`x gt y implies 1/x gt 1/y`

`x gt y implies (-1)/x lt (-1)/y`

If x and y are positive real numbers, then :

`xgtyrArr-xgt-y`

`x gt y rArr-x lt -y`

`x gt y rArr 1/x gt 1/y`

`xgtyrArr(-1)/xlt(-1)/y`