Chapter 1.6, Problem 24E

Identify the error or errors in argument that supposedly shows that if (

$\forall x\left(P\left(x\right)\vee Q\left(x\right)\right)$ is true then $\forall xP\left(x\right)\vee \forall xQ\left(x\right)$ is true.

1. $\forall xP\left(x\right)\vee Q\left(x\right)$ Premise

2. $P\left(c\right)\vee Q\left(c\right)$ Universal instantiation from (1)

3. $P\left(c\right)$ Simplification from (2)

4. $\forall xP\left(x\right)$ Universal generalization from (3)

5. $Q\left(c\right)$ Simplification from ()

6. $\forall xQ\left(x\right)$ Universal generalization from (5)

7. $\forall x\left(P\left(x\right)\vee \forall xQ\left(x\right)\right)$ Conjunction from (4) and (6)