UGC NET CSE | December 2015 | Part 3 | Question: 44

Question

In propositional logic, given $P$ and $P \rightarrow Q$, we can infer ________

• A. $\sim Q$
• B. $Q$
• C. $P \wedge Q$
• D. $\sim P \wedge Q$

Answer 1

Answer: B,C

Given premises: $P, P \rightarrow Q$

Valid Conclusion: $Q$ (By Modus Ponens rule of inference)

Transitively another Valid Conclusion: $P \wedge Q$ (By Conjunction rule of inference)

Answer 2

P -> Q  ans P infer to Q
 Using : Modus Ponens
B is answer

Answer 3

P  -> Q   = ~P  V Q

So we can infer Q

answer is B

Answer 4

if P then Q

P is given so we can infer Q

Answer 5

Ans: B

• Whenever E is a tautology, P1 AND P2 AND .. Pn -> E is a tautology.
• Given two premises P1 and P2, we can infer P1 AND P2.
• If P1 and (P1 -> P2) are given or inferred, then we can infer P2 by the rule of modus ponens (p AND (p->q) -> q).
• If NOT P2 and (P1 -> P2) are given or inferred, then we can infer NOT P1 by the rule of modens tollens.
• If P1 and (P1==P2) are given or inferred, we can infer P2.

ref: https://www.cs.rochester.edu/~nelson/courses/csc_173/proplogic/reason.html