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1) Consider the following predicates over the set U of stude

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1) Consider the following predicates over the set U of students.C(x): x is in the computer science classJ(x): x is a junior studentS(x): x is a senior studentCS(x): x is a computer science majorM(x): x is a math majorT(x,y): student x tutors student yRewrite the following statements in predicate logic using the given predicates.a) Junior students who are in the computer science class are either computer science majors or math majors.b) No senior student in the computer science class is a computer science major or math major.c) Every senior math major tutors some junior computer science major who is in the computer science class.d) Some senior computer science majors do not tutor any junior student who is in the computer science class.e) Mary is tutored by at least two senior students who are not in the computer science class.f) Every student in the computer science class is tutored by exactly one student who is a math major.2) Translate the following predicate logic statements into English using the definitions above.Image transcription text3. Determine the frequency counts for all statements in the following two algorithm sipmente for i:= 1 to n do while (i s a) do for jo= 1 to i do for ke= 1 to j do CHAPTER 1. INTRODUCTION AlgorithmTranspose(a, n) for f := 1 to n – 1 do for jud + 1 to n do Algorithm 1.24 Matrix transpose … Show more… Show moreBig O describes the growth rate of an algorithm proportional to the size of the inputs. This is one of the most important measurements for evaluating the suitability of an algorithm in a computer science application. Describe the steps of the bubble sort algorithm with emphasis on which steps contribute to the growth. Growth of the algorithm is how many programming operations must be performed to complete the task. Assume the worst case for the input array. (list all steps of algorithms and their descriptions)Image transcription text2- The density matrix of a pure quantum state [) is defined as p = [)(wland the density matrix ofthe collection of pure states [;) with the corresponding probabilities p, is defined as (a) Find adensity matrix of [ ) = = (100) + |11)) and show that this density matrix corresponds a … Show more… Show moreImage transcription text3- Considering the algorithm ; Obtain the output density matrix (Pout) of the first qubit in terms of thematrix elements of the input (Pin) density matrix of the first qubit of the algorithm given below where 0 == and Pin = c pal (Hint: Use partial trace operation to obtain Pout ) Pin Pout loXol Ry (0)… Show moreEngineering & TechnologyComputer ScienceCOMPUTER S COMP38411

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