Question

Suppose that both the program assertion$\mathbf{p}\left\{S\right\}{\mathbf{q}}_{\mathbf{0}}$and the conditional statement${\mathbf{q}}_{\mathbf{0}}\mathbf{\to }{\mathbf{q}}_{\mathbf{1}}$are true. Show that$\mathbf{p}\mathbf{\left\{}\mathbf{S}\mathbf{\right\}}{\mathbf{q}}_{\mathbf{1}}$also must be true.

Short answer

Yes, the$\mathrm{p}\left\{\mathrm{S}\right\}{\mathrm{q}}_1$ is true.

Step-by-step solution

Modus Ponens.

A rule of logic that says that if a conditional statement ('if p and q’s) is accepted and the antecedent is true, the consequent can be inferred. an argument using the modus ponens rule.

Step:-3 solution

Since$\mathrm{p}\left\{\mathrm{S}\right\}{\mathrm{q}}_0$is true, we know that p is true before S is executed. After S is executed, we know

that$q_0$is true. Since${\mathrm{q}}_0\to {\mathrm{q}}_1$is true given the problem and${\mathrm{q}}_0$is true from before, we

can conclude that ${\mathrm{q}}_1$is true using modus ponens

Hence,$\mathrm{p}\left\{\mathrm{S}\right\}{\mathrm{q}}_1$ is true.