Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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What is (a --> b) and (¬b --> c) and (¬ c↔¬b) logically equivalent to? Use logic laws and label them
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- Translate the following First Order Logic in English sentence. (Attached)arrow_forwardMathematical logic. From the study of the connectives (Unary and binary) proof the following sentence: Prove that {∧,↔,+} is complete but that no proper subset is complete. Please be as cleas as possible. Use definitions if necessary. Explain all the steps. Thank you.arrow_forwardRacket code only please Using the logical operators, and, or, implies, not, and iff, and atoms representing truth values, we can make a list that would represent proposition: For instance: '(A and (not A)), or '((B iff (A or C)) implies (not (C implies A))) would represent the formal statements (?∧¬?) and ((? ≡(?∨?)→¬(? →?))). We use the following convention when we represent propositions in this way: for every operator – unary or binary – there corresponds at least one pair of parentheses defining its scope (and perhaps more). Thus, the lists ‘(A and not A) and (B iff A or C) are not permitted but ‘((A and ((not A))) and ‘(B iff (((A or C)))) are acceptable. Define Evaluate-WFF, which will take as input a formula of prepositional logic in which there are only truth values and no propositional variables, such as the following: (#t or (not #t)). Evaluate-WFF should return #t if the formula under the particular truth assignment evaluates to #t and false otherwise. By way of example,…arrow_forward
- Racket code only please Using the logical operators, and, or, implies, not, and iff, and atoms representing truth values, we can make a list that would represent proposition: For instance: '(A and (not A)), or '((B iff (A or C)) implies (not (C implies A))) would represent the formal statements (A∧¬A) and ((B ≡(A∨C)→¬(C → A))). We use the following convention when we represent propositions in this way: for every operator – unary or binary – there corresponds at least one pair of parentheses defining its scope (and perhaps more). Thus, the lists ‘(A and not A) and (B iff A or C) are not permitted but ‘((A and ((not A))) and ‘(B iff (((A or C)))) are acceptable. 1. Define collect-prop-variables, which will take as input a list representing a proposition, and return a list, representing a set, of all the variables used in the expression. Example: (collect-prop-variables '(A and (not A))) should return '(A) and (collect-prop-variables '((B iff (A or C)) implies (not (C implies A))) )…arrow_forwardProve the following predicate logic statements valid or invalid: A) ∀x(A(x) → B(x)) ∧ ∀x(A(x) ∨ ¬C(x)) ∧ ∃x(¬B(x)) → ¬∃x(¬A(x) ∧ ¬B(x) ∧ ¬C(x)) B) ∀x(A(x) → B(x)) ∧ ∃x(A(x) ∨ B(x)) → ∃x(A(x) ∧ B(x))arrow_forwardIn modal logic, what is the duality between necessity and possibility? Provide examples of modal dualities.arrow_forward
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