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Identify the error or errors in this argument that supposedly shows that if ∃xP
(x) ∧ ∃xQ(x) is true then ∃x(P (x) ∧ Q(x)) is true.
a) ∃xP (x) ∨ ∃xQ(x) Premise
b) ∃xP (x) Simplification from (1)
c) P (c) Existential instantiation from (2)
d) ∃xQ(x) Simplification from (1)
e) Q(c) Existential instantiation from (4)
f) P (c) ∧ Q(c) Conjunction from (3) and (5)
g) ∃x(P (x) ∧ Q(x)) Existential generalization