UGC NET CSE | January 2017 | Part 2 | Question: 6

Question

In propositional logic if $\left ( P \rightarrow Q \right )\wedge \left ( R \rightarrow S \right )$ and $\left ( P \vee R \right )$ are two premises such that

$$\begin{array}{c} (P \to Q) \wedge (R \to S) \\  P \vee R \\ \hline Y \\ \hline \end{array}$$

$Y$ is the premise :

• A. $P \vee R$
• B. $P \vee S$
• C. $Q \vee R$
• D. $Q \vee S$

Comments

Why $ Y can't \; be\;P\vee R$ ??(which is obvious implication from premises)

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PVR is premise not conclusion e.g if p and p->q is given  what is the conclusion q  right

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Answer will be A,B,C,D. All the options are Valid Conclusions from the given premises.

Find detailed answer here:

https://gateoverflow.in/335157/ugc-net-cse-january-2017-part-2-question-6?show=390553#a390553 

Answer 1

Ans : D

 

Q∨S

This is based upon  constrctive dillema  rule of inference.

Answer 2

Both A and D are correct. Ofcourse if p+q holds true, we can conclude the same, so A is true as well.