I Finding useful denial (1 Viewer)

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Let U be universe under consideration, and let P(x) and Q(x) be predicate with free variable x. Find a useful denial for (∀x∈U)(P(x)⇒Q(x))

Then my answer is:

¬(∀x∈U)(P(x)⇒Q(x))

(∃x∈U)¬(P(x)⇒Q(x))

¬(P(x)⇒Q(x))

¬P∨Q

I'm unsure if I am on the write path when it comes to finding the useful denial, is this how to do it?

Thank you.
 

fresh_42

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Your last step is wrong.
$$
\lnot \,(P(x) \Longrightarrow Q(x)) \Longleftrightarrow \exists \,x_0 \in U \, : \,P(x_0) \wedge \lnot \,Q(x_0)
$$
 

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