Answer
After performing Simplification and Modus Ponens on the given set of statements it makes sense that the given statements are inconsistent i.e. we get that "Miranda is qualified for the job" becomes both true and false.
Work Step by Step
We can translate the given statements using the above interpretations. (Note: “but” can be interpreted as “and” in this case). The statements are inconsistent if we obtain that one variable is both true and false (which of course cannot be true).
Let us assume:
$p$= “Miranda takes a course in discrete Mathematics”
$q$= “Miranda graduated”
$r$= “Miranda is qualified for the job”
$s$= “Miranda reads this book”
STEP REASON
$(1)$ $\neg p \rightarrow \neg q$ premise
$(2)$ $\neg q \rightarrow \neg r$ premise
$(3)$ $s \rightarrow r$ premise
$(4)$ $\neg p \wedge s$ premise
$(5)$ $\neg p$ Simplification from $(4)$
$(6)$ $s$ Simplification from $(4)$
$(7)$ $\neg q$ modus ponens from $(1)$ and $(5)$ $(8)$ V $\neg r$ modus ponens from $(2)$ and $(7)$
$(9)$ $r$ modus ponens from $(3)$ and $(4)$
We obtained that r has to be true and $\neg r$ has to be true. However $\neg r$ is true when $r$ is false. Thus we obtained that $r$ is both true and false, which is impossible and thus the statements are inconsistent.
