Question # 5: Identify the error or errors in this argument that supposedlyshows that if ∃ xP ( x )∧∃ xQ ( x )is true then∃ x ( P ( x )∧ Q ( x ))is true. ∃ xP ( x )∨∃ xQ ( x ) Premise ∃ xP ( x )...

Question # 5:

Identify the error or errors in this argument that supposedlyshows that if ∃xP(x)∧∃xQ(x)is true then∃x(P(x)∧Q(x))is true.

1. ∃xP(x)∨∃xQ(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