Simplifying a Compound Statement

Question

I have to simplify $\neg(s \wedge(t \vee u ) \wedge ((s \wedge t) \rightarrow u))$

I started by trying to using $(p \rightarrow q) \iff \neg p \vee q$ and DeMorgan's laws but things got messy. Any suggestions?

Answer 1

DeMorgan is the way to start. You have a negated conjunction, which becomes the disjunction of the negation of the terms. Then a negated implication becomes a conjunction (of what?)

Answer 2

$$¬(s∧(t∨u)∧((s∧t)→u))$$

$$¬s v (¬t∧¬u) v (s∧t∧¬u)$$

$$¬s v (¬t∧t) v (s∧¬u∧¬u)$$

$$¬s v (F) v (s∧¬u)$$

$$¬s v (s∧¬u)$$

$$(¬svs) ∧ (¬sv¬u)$$

$$T ∧ (¬sv¬u)$$

$$(¬sv¬u)$$

(Final answer)

Did this question in a university class (just with different letters)