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. ∧
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The statement provided in the questions is
if is true then
TO support this arguments, These arguments are given
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
In step(1), there is an error in the Premise, as dis-conjunction is used instead of conjunction.
In step(5), It cannot be assumed that the same c makes the p as well as Q true as it is mentioned that p is true for the same value of n and Q is also true for some value of x, but it is not provided that both of them are true for the same value of x.