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

- $\sim$ Q
- Q
- P $\wedge$ Q
- $\sim$ P $\wedge$ Q

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**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

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