Predicate Logic Negating a WFF, do signs cancel?

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I'm working through an example for my course and I'm wondering if signs need to be canceled for this negation to be correct.

The original question is as follows --

(∀x)P(x) Λ Q(x)(R(x)-->W(x))

I believe the correct negation of this is as follows --

(∃x)P'(x) v Q'(x)(R(x) v W'(x))

The question I have is, assuming I took the correct steps here, would the R's negation symbol cancel out since DeMorgan's law would be applied to turn the implication into a disjunction, then the outside negation symbol would distribute in on the R and W where the R would already have a negation symbol?