Determine Consistency Of System Specifications

Let $b$ stand for the diagnostic message is stored in the buffer, and let $r$ stand for the diagnostic message is re-transmitted. The three statements can then be abbreviated $b\lor r$, $\lnot b$, and $b\to r$. The question is then whether there is an assignment of truth values to $b$ and $r$ that makes all three statements true. If there is not, they’re mutually inconsistent; if there is, they’re consistent, though they may be satisfied for only one possible assignment of truth values to $b$ and $r$. Indeed, that turns out to be the case here:

$$\begin{array}{cc} b&r&\lnot b&b\lor r&b\to r\\ \hline \text{T}&\text{T}&\text{F}&\text{T}&\text{T}\\ \text{T}&\text{F}&\text{F}&\text{T}&\text{F}\\ \color{red}{\text{F}}&\color{red}{\text{T}}&\color{red}{\text{T}}&\color{red}{\text{T}}&\color{red}{\text{T}}\\ \text{F}&\text{F}&\text{T}&\text{F}&\text{T} \end{array}$$

As you can see, they are consistent, but they hold simultaneously only when $b$ is false and $r$ is true.