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Answer the following questions . [15 marks] Consider the following set of known facts and rules f...
Consider the schema R = (A, B, C, D, E) and let the following set F of functional dependencies holdforR: F = {A -> BC, CD -> E, C -> A, B -> D,} 1) Prove or disprove ADE is in the closure of F. A proof can be made by using inference rules IR1 through IR3. A disproof should be done by showing a relational instance (counter example) that refutes the rule. 2) What are the candidate keys of...
Logic Programming An important type of programming language is designed to reason using the rules of predicate logic. Prolog (from Programming in Logic), developed in the 1970s by computer scientists working in the area of artificial intelligence, is an example of such a language. Prolog programs include a set of declarations consisting of two types of statements, Prolog facts and Prolog rules. Prolog facts define predicates by specifying the elements that satisfy these predicates. Prolog rules are used to define...
I want to know the answer and explanation of (d) and (f). 2. Percentiles and Quartiles Given a data set with n data values yvi < /2 ..S yn, define the pth percentile of the data set to be the element at index ceiling, and it means that we always round up to the next integer. For example, suppose we have a data set with n - 13 elements, and we want to calculate the 25th percentile of the data...
4. Assume the following rules of associativity and precedence for expressions: Precedence Highest *, /, not +,-,&, mod - (unary) =,/=,<,<=,>=,> and or, xor Lowest Associativity Left to right Show the order of evaluation of the following expressions by parenthesizing all sub expressions and placing a superscript on the right parenthesis to indicate order. For example, for the expression a+b*c+d the order of evaluation would be represented as ((a+(b*c)1)2 +d)3 a * b - 1 + c a * (b...
2. 9 marks] Strings. Consider the following definitions on strings Let U be the set of all strings Let s be a string. The length or size of a string, denoted Is, is the number of characters in s Let s be a string, and i e N such that 0 < ί < sl. We write s[i] to represent the character of s at index i, where indexing starts at 0 (so s 0] is the first character, and...
2. 9 marks] Strings. Consider the following definitions on strings Let U be the set of all strings. Let s be a string. The length or size of a string, denoted Is, is the number of characters in s Let s be a string, and ie N such that 0 Si< Is. We write si] to represent the character of s at index i, where indexing starts at 0 (so s(0 is the first character, and s|s -1 is the...
Problem #2: Consider the following statements. [6 marks) (1) The particular solution of the ODE)" - 6y' + 9y = 5e3x is given by yp = Cre3x where C is an undetermined constant. (ii) The procedure of finding series solutions to a homogeneous linear second-order ODEs could be accurately described as the "method of undetermined series coefficients". (iii) Most of the material in Lecture Notes from Week 3 to Week 5, inclusive, can be extended or generalized to higher-order ODES...
Please answer the following questions with solution, thanks 4. Consider the function f(x) = 2x + 1, a) Find the ordered pair (4. f(4) on the function. b) Find the ordered pair on the inverse relation that corresponds to the ordered pair from part a). c) Find the domain and range of f. d) Find the domain and the range of the inverse relation off. e) Is the inverse relation a function? Explain. 5. Repeat question 4 for the function...
Problem #5: [3 marks] Let u and y be vectors in R. Consider the following statements. (i) u vl = ||0|| + ||v|| (ii) ||u + v||2 = ||u||2 + ||v||2 + 2(u'v) (iii) If au + bv = cu + dv and a, b, c, and d are all nonzero then u = 0 and v=0. Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the...
Colors Fonts Set as Default Document Formatting Answer the following questions: Question 1. [3+5=8 Marks] Random samples have been selected from two normally distributed populations with equal variances. The following sample data were observed, Samples from population 1 Samples from population 2 a) Find a 90% confidence interval for the difference between two population means. b) Use a significance level of 0.10 for testing the hypothesis 11 HH2 10. (United States) Question 2. [3+4-7 Marks) Historical data indicates that the...