Choose two of the arguments below and write a direct proof using the eight rules of inference introduced in section 8.1 of the textbook. You can do argument 1 or argument 2, but not both, then any of arguments 3–6. Note that commas are used to separate the premises from each other. ~M, (~M • ~N) → (Q → P), P → R, ~N, therefore, Q → R ~F → ~G, P → ~Q, ~F v P, (~G v ~Q) → (L • M), therefore, L ~(Z v Y) → ~W, ~U → ~(Z v Y), (~U → ~W) → (T → S), S → (R v P), [T → (RvP)] → [(~R v K) • ~K], therefore, ~K (S v U) • ~U, S → [T • (F v G)], [T v (J • P)] → (~B • E), therefore, S • ~B ~X → (~Y → ~Z), X v (W → U), ~Y v W, ~X • T, (~Z v U) → ~S, therefore, (R v ~S) • T (C → Q) • (~L → ~R), (S → C) • (~N → ~L), ~Q • J, ~Q → (S v ~N), therefore, ~R Natural deduction is so called because it is a model for how we naturally reason. The symbols allow us to focus on the form of the argument, allowing for clarity of reasoning. We should be able to translate our symbols into natural language. Each sentence letter represents a simple sentence in English. After writing your direct proofs, construct a translation key for your argument by assigning each letter a simple sentence, and use that key to fill in the content of the argument

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Choose two of the arguments below and write a direct proof using the eight rules of inference introduced in section 8.1 of the textbook. You can do argument 1 or argument 2, but not both, then any of arguments 3–6. Note that commas are used to separate the premises from each other.

~M, (~M • ~N) → (Q → P), P → R, ~N, therefore, Q → R
~F → ~G, P → ~Q, ~F v P, (~G v ~Q) → (L • M), therefore, L
~(Z v Y) → ~W, ~U → ~(Z v Y), (~U → ~W) → (T → S), S → (R v P), [T → (RvP)] → [(~R v K) • ~K], therefore, ~K
(S v U) • ~U, S → [T • (F v G)], [T v (J • P)] → (~B • E), therefore, S • ~B
~X → (~Y → ~Z), X v (W → U), ~Y v W, ~X • T, (~Z v U) → ~S, therefore, (R v ~S) • T
(C → Q) • (~L → ~R), (S → C) • (~N → ~L), ~Q • J, ~Q → (S v ~N), therefore, ~R

Natural deduction is so called because it is a model for how we naturally reason. The symbols allow us to focus on the form of the argument, allowing for clarity of reasoning. We should be able to translate our symbols into natural language. Each sentence letter represents a simple sentence in English.

After writing your direct proofs, construct a translation key for your argument by assigning each letter a simple sentence, and use that key to fill in the content of the argument

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