Hypotheses: not $q$, $p$ or not $s$, $p \rightarrow$ ($d$ and $q$), $e \rightarrow s$
Conclusion: not $e$
I have thus far, but unsure how to proceed. I am looking forward to solve it using tautologies.
$1)$ not $q$ as premise
$2)$ $p$ or not $s$ as premise
$3)$ $p \rightarrow$ ($d$ and $q$) as premise
$4)$ $e \rightarrow s$ as premise
$5)$ $(d$ and $q)$ implies $q$ is true by simplification.
$6)$ $(d$ and $q)$ implies $q)$) and not $q$ implies not $(d$ and $q)$ by Modus Tollens
$1)$ $\lnot q$ as premise
$2)$ $p$ or $\lnot s$ as premise
$3)$ $p \rightarrow$ ($d\land q$) as premise
$4)$ $e \rightarrow s$ as premise
$5)$ $\quad p\quad$ Assumption
$6)$ $\quad d \land q\;$ (3, 5) by modus ponens
$7)$ $\quad q\;$ by simplification (6)
$8)$ $\quad q \land \lnot q\;$ (1, 8) (And-introduction)
$9)$ $\lnot p$, since assumption $p$ leads to a contradiction (5-8)
$10)$ $ \lnot s,$ from 2, 9 Disjunctive syllogism
$11)$ $\lnot e$ from 4, 10 by modus tollens.