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.

Question

1.∃x(P(x)∧Q(x)) Premise

2.∃xP(x) Simplification from (1)

3.P(c) Existential instantiation from (2)

4.∃xQ(x) Simplification from (1)

5.Q(c) Existential instantiation from (4)

6.P(c)∧Q(c) Conjunction from (3) and (5)

7.∃x(P(x)∧Q(x)) Existential generalization

Answer 1

Kai, first line of the proof is inaccurate.

your problem statement says that the premise is

∃xP(x) ∧ ∃xQ(x)

but the first line of the proof says

∃x (P(x) ∧ Q(x) )



claiming that is the Premise. It is not.