Q1:  a) For how many n ∈{ 1,2,...,500} is n a multiple of one or more of 5, 6, or 7?         b) For how many n ∈ {1,2,...,500} is n a multiple of one or more of 5, 6 ?   Please use this formula for both ques formula : n(A+B+C) = n(A) + n(B) + n(C) - n(AB) -n(AC) -n(BC) + n(ABC) [ this formula is for 3 digit numbers]   { what will be foemula for 2 digits ) please make it clear. ty

Q: Solve the following recurrence relation using master’s method. T(n) = 3T(n/2) + n^2

A: Given Relation is T(n) = 3T(n/2) + n^2 . It is solved using master's method.

Q: Determine the value of No and constant C so that one can expression the following function can be…

A: Big O notation is a mathematical notation that describes the worst-case scenario of an algorithm's…

Q: The following questions will be based on the recurrence relation: T(n) = 16T([n/4]) + 3n if n > 4…

A: 1) Given equation is in the form of T(n)=aT(n/b)+nklogpn where a=16, b=4, k=1 and p=0, so masters…

Q: If A = {1,2,3,4,5} and B ={4,5,6,7,8} then B-A is {1,2,3} {6,7,8} (4,5} { 1,2,3,4,5,6,7,8}

A: I have given an answer in step 2.

Q: 3. Find AB if Г2 a) A В - 3 2 3

A: There is 2 row and 2 col in both matrix The number of columns of the 1st matrix must equal the…

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A: Solution ::  Let's see first what is thread and its uses ?  Answer ::  In computer science, a thread…

Q: Algorithm 1 exp(a, n): compute a" for integer a and n ≥ 0 if n = 0 then return 1 end if x if n is…

A: A recursive is given in the problem statement and it is asked to create the recurrence relation for…

Q: Solve the recurrence relation without master's theorem : T(n)= 7T(n/2)+ n^2

A: The above given that is T(n)= 7T(n/2)+ n^2 is a form of divide and conqure method in which we have…

Q: Order the following functions by order of growth, that is, if a function f is listed before a…

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Q: 1.) Please prove the following using definitions. a.) 2n4 − 5n2 ∈ Θ(n4) b.) n log n − n ∈ Ω(n log…

A: Proved the given functions of the asymptotic notations

Q: 4. Using the substituion method and T(1) = 0, solve the following recurrence relations a) T(n) =…

A: a)

Q: Write a set that is result of the following operation: a. (ANB) U C b. (Bx C) (Cartesian product)…

A:

Q: c) Prove that the following claim holds when for all n ≥1 Σ(8i-5)=4n²- n i=1 n

A: SOLUTION - In this problem, we need to prove : ∑i=1n(8i−5)=4n2−n   PROOF -   Taking left-hand side,…

Q: Solve the recurrence relation: T (n) = T (n/2) + T (n/4) + T (n/8) + n. Use the substitution method,…

A:

A potential method of analysis

The complexity of the algorithm model emphasizes the potential method. This method is useful for examining a data structure's amortized time and space complexity.