Let predicate function P$($k$,$s$)$s$^2<=$k$<=($s$+1)^2.$ For each of the following triples, decide whether it is valid $($under either correctness$),$ justify your answer briefly.

$\{$P$($k$,$s$+1)\}$ s$$s$+1\{$P$($k$,$s$)\}$

$\{$P$($k$,$s$)\}$ s$$s$+1\{$P$($k$,$s$+1)\}$

$\{$P$($k$,$s$)$s$<0\}$ s$$s$+1$;k$$k$+1\{$P$($k$,$s$)\}$

$\{$P$($k$,$s$)$s$=$s$\_0\}$ s$$s$+1\{$P$($k$,$s$\_0)\},$ where s$\_0$ represents the value of s in the precondition.

$\{$P$($k$+1,$s$+1)\}$ s$$s$+1$;k$$k$+1\{$P$($k$,$s$)\}$