Answer
The error in this argument is in step 7:
Work Step by Step
The argument attempts to conclude that ∃x(P(x) ∧ Q(x)) is true, but this is not a valid inference. Existential generalization is the process of inferring the existence of an unspecified object that satisfies a particular condition. However, the argument fails to provide sufficient justification for this conclusion.
In the given argument, the premises show that there exist specific values of x for which P(x) and Q(x) are true (P(c) and Q(c) for some constant c), but it doesn't prove that there exists an x for which both P(x) and Q(x) are simultaneously true for any arbitrary x. Therefore, step 7 is not valid.
