State which of the following statements is true of false.
(i) If ` x lt y and b lt 0," then "x/b lt y/b`.
(ii) If `xy gt0," then "xgt0and ylt0`
(iii) If `xy gt0," then "xlt0 and ylt0`
(iv) If `xylt0," then "xlt0and ylt0`
(v) If `xlt-5and xlt-2," than "x in (-infty,-5)`
(vi) If `xlt-5 and xgt2," then "x in (-5,2)`
(vii) If `xgt-2and xlt9,"then "x in (-2,9)`
(viii) If `|x|gt5," then " x in (-infty,-5) cup [5, infty)`
(ix) If `|x|le4," then "x in [-4,4]`
(x)` "Graph of "x lt 3 `is

(xi) Graph of `x ge 0` is

(xii) Graph of `y le 0` is

(xiii) Solution set of `x le 0 and y le 0` is

(xiv) Solution set of `x ge 0 and y le 1` is

(xv) Solution set of ` x + y ge 0` is

Explanation

(i) If ` x lt y and b lt 0`
`rArr x/b gt y/b`
Hence, statement (i) is false.
(ii) If ` x y gt 0," then "0, y gt 0 or x lt 0, y lt 0`.
Hence, statement (ii) is true.
(iii) If `x y gt0," then "x lt 0 and y lt 0`.
Hence, statement (iii) is true.
(iv) If `xy lt 0 rArr x lt 0, y gt 0 or x gt 0, y lt 0`.
Hence, statement (iv) is false.
(v) if `x lt - 5 and x lt - 2`, then
`x in (-infty, -5)`
Hence, statement (v) is true.
(vi) If ` x lt - 5 and x gt 2`, then x have no value.
Hence, statement (vi) is false.
(vii) If ` x gt-2 and x lt 9," then "x in (-2,9)`.
Hence, statement (vii) is true.
(viii) If ` |x| gt 5," then either "x lt - 5 or x gt 5`.
`rArr x in (-infty, -5) cup (5, infty)`
Hence, statement (viii) is false.
(ix) If ` |x| le 4`, then
` -4 le x le 4`
`rArr x in [-4, 4]`
Hence, statement (ix) is true.
(x) The given graph represents `x le 3`.
Hence, statement (x) is false.
(xi) The given graph represents ` x ge 0`.
Hence, statement (xi) is true.
(xii) The given graph represent `y ge 0`.
Hence, statement (xii) is false.
(xiii) Solution set of ` x ge 0 and y le 0` is

Hence, statement (xiii) is false.
(xiv) Solution set of ` x ge 0 and y le 1` is

Hence, statement (xiv) is false.
(xv) The given graph represents ` x + y ge 0`.
Hence, statement (xv) is correct.