Consider the following “proof" 1: a ^ (¬a → b) (Premise) 2: a ^ (¬a V b) (Implication, 1) 3: (a ^ ¬a) V b (Associative, 2) 4: T V b (Negation, 3) 5: T (Identity, 4) (a) Identify all of the errors in the proof. (b) Using Rules of Inference and Propositional Equivalences, formally prove that a ^ (¬a → b) = a

Consider the following “proof" 1: a ^ (¬a → b) (Premise) 2: a ^ (¬a V b) (Implication, 1) 3: (a ^ ¬a) V b (Associative, 2) 4: T V b (Negation, 3) 5: T (Identity, 4) (a) Identify all of the errors in the proof. (b) Using Rules of Inference and Propositional Equivalences, formally prove that a ^ (¬a → b) = a

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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Answer only question 15
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Calculate (by hand) the appropriate truth table to prove the following: (¬q → ¬p) ∧ p ⇔ p ∧ q Explain why your truth table shows that this is an equivalence and prove it using the fundamental logical equivalences given in Tables 7.6–7.7 in the Unit Notes (reproduced below for convenience).[Hint: Start by using the contrapositive equivalence.]
Say whether the following are correct. If yes, provide a natural deduction proof. If not, provide a counterexample. P → Q ` (R → P) → (R → Q) This is incorrect. but what is a counterexample?
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Find the errors and identify them. Put ‘x’ next to the line with errors and the number of the errors using the List of Errors in Predicate Logic Proofs document. (x) (y) Fxy > (Ez) Hxz Premise (Ev) Hxv Premise Hxx Existential Instantiation (2) (y) Fxy > (Ez) Hxz Universal Instantiation (1) Fxy > (Ez) Hxz Universal Instantiation (4) Fxy > Hxv Existential Instantiation (5) Fxy Modus Ponens (3,6) (Ex) Fxx Existential Generalization (7) (Ex) Fxx v ~ (Ex) Fxx Add (8) (Ex) Fxx Disjunctive Syllogism (8,9)
Please answer question 2 thank you
Use semantic tableau and truth tables (2 separate proofs) to determine whether the conclusion of the following argument follows from the premises. P→ (¬H→C) (P→ ¬H)/(P→ C)
Show that the argument is valid, indicating the rule of inference or logical equivalence applicable to each step. ∃x ( C(x) ∧ ( ¬ S(x) → ( V(x) ∨ W(x) ) ) )∀x ( V(x) → ¬ C(x) )¬ ∃x ( W(x) ∧ C(x) ) _________________________∴ ∃x ( S(x) ∧ ¬ W(x) )
Apply a series of logical equivalences and/or rules of inference to show that r → q follows from the following premises. Be sure to indicate the line number(s) and logical equivalence or rule of inference used in each step. 1. p → q 2. (r V s) → p 3. ¬s