UGC NET CSE | October 2020 | Part 2 | Question: 40

Question

Consider the following argument with premise $\forall _x (P(x) \vee Q(x))$ and conclusion $(\forall _x P(x)) \wedge (\forall _x Q(x))$

$\begin{array}{|ll|l|} \hline (A) & \forall _x (P(x) \vee Q(x)) & \text{Premise} \\ \hline (B) & P(c) \vee Q(c) & \text{Universal instantiation from (A)} \\ \hline (C) & P(c) & \text{Simplification from (B)} \\ \hline (D) & \forall _x P(x) & \text{Universal Generalization of (C)} \\ \hline (E) & Q(c) & \text{Simplification from (B)} \\ \hline (F) & \forall _x Q(x) & \text{Universal Generalization of (E)} \\ \hline (G) & (\forall _x P(x)) \wedge (\forall _xQ(x)) & \text{Conjuction of (D) and (F)} \\ \hline \end{array}$

• A. This is a valid argument
• B. Steps $(C)$ and $(E)$ are not correct inferences
• C. Steps $(D)$ and $(F)$ are not correct inferences
• D. Step $(G)$ is not a correct inference

Answer 1

option B is right ans  Steps (C) and (E) are not correct inferences

   

 as in Step (C)  we can not  infer P(C) from P(C)V Q(C) { it only means at least one of them is true)

        

and similarly in Step (E) we can not  infer Q(C)  from P(C)V Q(C)     

Rest are all ok