kenneth h rosen chapter 1 excercise 1.4 predicated and quantifiers question 19
in Mathematical Logic
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Suppose that the domain of the propositional function
P (x) consists of the integers 1, 2, 3, 4, and 5. Express
these statements without using quantifiers, instead using
only negations, disjunctions, and conjunctions.

  1. ∀x((x = 3) → P (x)) ∨ ∃x¬P (x)

so i write like this see image

image
so my doubt is how above solution is written in simply way 

how he writes this answer → P(l) /\ P(2) /\ P(4) /\ P(5)) V (•P(l) v-.P(2) v-.P(3) V •P(4) V •P(5)) there is no P(3) inside this equation

please help 

 

 

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