The following \"proof\" attempts to show that premises P_1 and P_2 imply conclus

Question

The following "proof" attempts to show that premises P_1 and P_2 imply conclusion C. However, it contains a flow. Identity the setp that contains the flaw and explain what is wrong. P_1: there exists_x(P(x) Q(x)), P_2: there exists_x(Q(x) rightarrow R(x)), C: there exists_x(P(x) R(x)) there exists_x(P(x) Q(x)) Premise there exists_x(Q(x) R(x)) Premise P(c) Q(c) P(c) Q(c) Q(c) rightarrow R(c) R(c) P(c) R(c) there exists_x(P(x) R(x) 1, Existential Instantiation 3, Simplification 3, Simplification 2, Existential Instantiation 5, 6, Modulus Ponens 4, 7, Conjunction 8, Existential Generalization

Explanation / Answer

The Step No. 6 is incorrect as Existential Instantiation may or may not be possible for c which is an element of x.So the premise 2 might not be true for c as it is one of the elements.If it had been for all elements in premise 2 , it would have been correct.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---