Identify the error or errors in this argument that
Chapter 7, Problem 23E(choose chapter or problem)
Identify the error or errors in this argument that supposedly shows that if \(\exists x P(x) \wedge \exists x Q(x)\) is true then \(\exists x(P(x) \wedge Q(x))\) is true.
1. \(\exists x P(x) \vee \exists x Q(x)\) Premise
2. \(\exists x P(x)\) Simplification from (1)
3. \(P\) (c) Existential instantiation from (2)
4. \(\exists x Q(x)\) Simplification from (1)
5. \(Q\) (c) Existential instantiation from (4)
6. \(P\) (c) \(\wedge Q\) (c) Conjunction from (3) and (5)
7. \(\exists x(P(x) \wedge Q(x))\) Existential generalization
Equation Transcription:
∃xP (x) ∧ ∃xQ(x)
∃x(P (x) ∧ Q(x))
∃xP (x) ∨ ∃xQ(x)
∃xP (x)
∃xQ(x)
P (c) ∧ Q(c)
∃x(P (x) ∧ Q(x))
Text Transcription:
\exists x P(x) \wedge \exists x Q(x)
\exists x(P(x) \wedge Q(x))
\exists x P(x) \vee \exists x Q(x)
\exists x P(x)
\exists x Q(x)
\exists x(P(x) \wedge Q(x))
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer