If p is false, then P→(Q→R) is a true proposition;

If p is true, then when q is false, then P→(Q→R) is a true proposition; Then Q→(P→R) is also a true proposition;

If P is true, Q is true and R is true, then P→(Q→R) is a true proposition; Then Q→(P→R) is also a true proposition;

If P is true, Q is true and R is false, then P→(Q→R) is a false proposition; Then Q→(P→R) is a false proposition.

Based on the above results, in each case, the truth values of the two propositions are the same, so the two propositions are equivalent.

Construct the following reasoning proofs in the natural reasoning system P:

Premise: A ∨ B → C ∧ D, D ∨ E → F.

Conclusion: A→F

① A∨B→C∧D premise

② Simplified formula of c ∧ d → d

③ A∨B→D premise syllogism ① ②

④ A→A∨B addition formula

⑤ D→D∨E addition formula

6 d ∨ e → f premise

All landowners A ∨ B → F premise syllogism 356

⑧ A→F premise syllogism ④ ⑦

Proof: (A-B)-C=A-(B∪C)

(A-B)-C=A-(B∪C)

A-B-C=A-(B+C)

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