Question $4$

$4\mathrm{.}1$ Suppose there are two integer values i and $p.$ Calculate what must be assigned to $p$ to maintain invariant the sum $i+p$ under the increment of $i$ by $1.$ In other words, calculate $x$ such that for arbitrary $C$

$\{i+p=C\}i,p$:$=i+1,x\{i+p=C\}$

$4\mathrm{.}2$ Suppose there are three program variables $a,b$ and $z.$ Calculate the assignments to a so that the following invariant is maintained:

$z+ab=C$

In other words, calculate $x$ such that

$3$

COS$4892/102$

$\{z+ab=C\}z,a$:$=z+b,x\{z+ab=C\}$