7. [6 marks, 3 marks each] a) is the following schema a derived rule of our...
Is the following schema a derived rule of our logic (that is, of logic 1 or 2)? A → B ⊢ A → (∀x)B - If you think that it is, then give a proof in our logic - If you do not think so, then give a definitive reason as to why-for example, using a concrete interpretation, or by proving the invalid “strong generalization” using (2) as a lemma.
3. (6 marks: 3 marks for steps, 3 marks for labels]+Simplify the following statement using the laws and axioms of logic. Clearly state which law or axiom has been used at each step. 4 [4+4-8 marks] Given the following statements: The student is in the esports club or in the aquatic club. if they are in the esports club then they do not get free access to the pool. The student does get free access to the pool. Therefore the...
Logic Discrete Maths Question 3 & 4 3. [6 marks: 3 marks for steps, 3 marks for labels] Simplify the following statement using the laws and axioms of logic. Clearly state which law or axiom has been used at each step 4. [4 +4-8 marks] Given the following statements The student is in the esports club or in the aquatic club. If they are in the esports club then they do not get free access to the pool. The student...
Question 6 [10 marks a) Let f(x) = x for each xe [a,b]. Show that for any number of subintervals, the global error js(x)dx-SUS J) = 0. [6] Hint: Obtain the local error first and then calculate the global error. SCS ,h) denotes approximation using the composite Simpson's Rule. b) Determine the minimum number of subintervals so that the upper bound of the (absolute) global error for the composite Simpson's Rule applied to ja?-10x”) dx is less than 10%. [41...
(b) Using the Davis-Putnam-Logemann-Loveland (DPLL) algorithm, determine whether the following formula is satisfiable. Show each step. [3 marks] (c) Give an example of a conjunctive normal form (CNF) formula where the pure literal rule can be applied, but the unit propagation rule cannot. The formula must have at least 3 clauses. [3 marks (b) Using the Davis-Putnam-Logemann-Loveland (DPLL) algorithm, determine whether the following formula is satisfiable. Show each step. [3 marks] (c) Give an example of a conjunctive normal form...
1. (6 marks) Provide the domain, target, and range of the following functions (a, b, c, d}3 . For each x E(a, b, cF, fx)-dx. a) fta, b. c}2 b) g: {a, b, c, d)-(a, b, c, d}?. For each x E(a, b, c, d], g(x) (4 marks) Use the ceiling and floor functions to qive a mathematical expression for the following a) Among a random group of 100 people at least 9 must be born in the same month...
f Question 1 (40 marks) (Compulsory) Answer each sub-question, a) to j). Long answers or explanations are not required. Full marks will be awarded for succinct, comect answers, whether as mathematical expressions, suitably labelled dlagrams, or brief text. If you use standard symbols in your answers there is no need to spend time defining them, unless asked to do so. a) Explain why the direction of the velocity of a particle is tangential to its trajectory. [4 marks] b) What...
HICULTUULUULULUI 2 Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points 1 - ...) a | and B(x) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: . This part of the assignment is testing that you can find the equation of a line and use this...
Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points A(Y) and (.ya) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: • This part of the assignment is testing that you can find the equation of a line and use this to derive other formulae. Marking Criteria...
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