A set of statements are called Logical Inconsistent when they can't be true at the same time.
For example, If we have some statements as $p,q,r,s$ then if we make a set of some logical statements from these statements $p,q,r,s$ like $\{p \rightarrow \;\sim q , r\rightarrow q, \;\sim p \rightarrow r\}$ then this set of logical statements i.e. $\{p \rightarrow \;\sim q , r\rightarrow q, \;\sim p \rightarrow r\}$ is called logically inconsistent if it can't be true at the same time and logically consistent if we can get at least one possible set of boolean values of $p,q,r,s$ for which all the statements from the set $\{p \rightarrow \;\sim q , r\rightarrow q, \;\sim p \rightarrow r\}$ are true simultaneously. We can check it by making truth table also. In truth table if we get atleast one tuple for which all the statements of the set $\{p \rightarrow \;\sim q , r\rightarrow q, \;\sim p \rightarrow r\}$ are true then this set is called logically consistent otherwise logically inconsistent.
Now, In this question,
Let,
$p$ = Miranda does not take a course in Discrete Mathematics
$q$ = She will not graduate
$r$ = She is not qualified for the job
$s$ = She reads this book
Now, according to given statements in the question,
We have to check logical consistency for the set :-
$\{p\rightarrow q,\; q\rightarrow r,\;s\rightarrow \sim r, \; p\wedge s\}$
Now, I am trying to make it consistent and checking that I will get success or not for this goal.
For logical consistency, all statements must be true simultaneously.
So, statement $p\wedge s$ must be true. It means both $p$ and $s$ must be true.
Now, statement $s\rightarrow \sim r$ should also be true , So, $r$ must be false.
and if $r$ is false then statement $q\rightarrow r$ must be false.
So, all statements can't be true at the same time.So, It means I have failed in my goal.
So, We can conclude that given set of logical statements is logically inconsistent.
