Show that 2n  E  O(3n).

Q: find lim X Sin (1/x)

A:

Q: 3. Try to obtain a closed form for the following recurrence equation: if n 4. |

A: Given p0 = 1 p1 = 1 p2 = 1 p3 = 3 p4 = p3 + (4-1)p2 - p1 + p0        = 3+3*1-1+1  = 6 p5= p4+ 4p3-…

Q: Prove that the n-cube Qn is a Hamiltonian graph for all n ≥ 2.

A:

Q: Find the symmetric closure of R.

A: Given To know symmetric closure of R.

Q: Prove that A → B E (Vx)A → (Vy)B, if y is not free in B.

A:

Q: H.W:- Find the determinant for the following matrices: [0.1 0.1 -4.3] 6. E =7.5 lo.3 6.2 0.7 answer:…

A: Here in this question we have given a determinant and we have asked to find the determinant of this…

Q: (cos n) Find the limit of the sequence an 3n

A: Answer

Q: 6 = 0 i = ab

A: Proved the validity of the given set of functions, reduced to minimum SOP form

Q: Prove that 2n = o(22n).

A:

Q: Prove Equationally that for any A and B A, ¬AFB = -¬B

A: We have to prove that Equationally that for Any A and B    A,  ~A l- B = ~B

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…

Q: Lim メ+ -2 Find this limit メや0

A:

Q: lim メーやO Find this limit メ+H -2

A:

Q: Prove that: A + A. B = Ã + B

A: This is because of the Distributive property of the boolean algebra which states that the boolean…

Q: Use the Pumping Lemma with length to prove that the following language is non-regular: L = {a²bn an,…

A: We need to prove that L is non-regular, using Pumping lemma.

Q: 1. Prove that for any k>0, nk e o(2v).

A: Solution:-.       1.).    Any k>0,n^k€2^√n

Q: • Let F(x, y, 3) = x²yi - (2²-3x) 5+uy³k. Find the divergence and curl of F.

A: Divergence and curl: Divergence and curl are two measurements in the vector field. Both measurements…

Q: Prove that L+ = L* if and only if ɛ ∈ L.

A: The main difference between L+ and L* is epsilon.

Q: Solve for x: 7x = 3 mod 11

A: The question is to solve for x: 7x ≡3 mod 11

Q: Reduce the following using K-Map. Obtain using Sum of a Product. 1. Σ(0,1,4,5,10,11,12,13,15)

A: Map   C.D C.D C.D C.D A.B 1 1 0 0 A.B 1 1 0 0 A.B 1 1 1 0 A.B 0 0 1 1 Map Layout…

Q: Consider the elliptic curve group based on the equation. where a = 33, b = 5, and p = 53. y² = x³ +…

A:

Q: HiWi Findd XCn) if: 2 X (z)= 3 (7-2)

A: - We need to find the value of x(n) based on the equation provided. - We will write a program to…

Q: 1o find 2 (-1) n- (n+i) by using for in c++

A: Use a for loop for iterating value of n from 1 to 10 and keep on adding each term to sum which is…

Q: Use the Pumping Lemma to show that L {wwRw E E*} is not a regular languag

A: Pumping CFL lemma states for each sense of Free Language, that two substrates can be pumped in one…

Q: u have a C rided into 2 given to h

A: Class C has range from 192-223 25 subnets means 2^5 =32So answer is 5 bitsoption C

Q: Consider the elliptic curve group based on the equation y² = x³ + ax + b mod p where a = 645, b=…

A:

Q: 7, Prove that if G is a group of order 1045 and HE Syl₁9 (G), K € Syl₁1 (G), then KG and HC Z(G).

A:

Q: Prove that {02"|n 2 1 and n E N} is not regular using the Pumping Lemma

A: Here, I have to prove the given language is not regular using pumping lemma.

Q: Show that if G=lV, E) is connected, gooph then %3D

A: Given  graph G=(v,e)

Q: Construct R.e from given OFA

A: Given Data:- To  Construct RE from given DFA

Q: Prove the following equivalencies by reducing each side to its normal form. a. I = SK K b. S K K = K…

A: Given, I on the left and SKK on the right, we have I = SKK.Now, Consider SKK is reduced to SK and…

Q: Find a minimum product-of-sums solution for f. Underline the essential prime implicants. Ma, b, c,…

A: Given 5 variables function is, f(a, b, c, d, e)=Σm(2,4,5,6,7,8,10,12,14,16,19,27,28,29,31)+Σd(1,30)…

Q: Prove that v(P) = 2,

A:

Q: Construct R.e from given OFA 0,1

A: The Answer is

Q: Prove that 2" = o(22n). %3D

A:

Q: Construction of an NFA N to recognize A¡ L A2

A: Explanation has been giving in the image. See below the step.

Q: Prove that 14n is not O(12n)

A: Given that  Prove that 14n ≠ O(12n )

Q: (a) Let H, K be subgroups of a group with identity e, such that |H| = 20 and |K| = 45. Determine |H…

A: According to the information given:- We have to define and prove the |H intersection K| not equals…

Q: Given that h(p)=p2−4p+7, Find;h(x-4)

A: Answer: h( x - 4 ) = x 2 - 12x + 39.

Q: prove it is non-regular using pumping lemma d. L = {xyx | x, y e {a, b}* and |x| > 1}

A: Proved the given language is regular or none regular

Q: Show that the Catalan number Cn satisfies the recurrence relationship (n + 1)Cn = (4n – 2)Cn-1, n>…

A:

Q: Let, a1 = 3 and for n > 2, an 2an-1+5, express an in terms of n.

A: We are going to solve given recurrence relation and express an in terms of n. Using substitution…

Q: 2. Let C Ç RE be such that Ø E C. Prove that Lc = {{M): M is a TM and L(M) e C} ¢ RE.

A: According to the question ,  we have given that Regular expression belongs to C and we have to prove…

Q: QUESTION 3 Find k, if any, such that AB= BA where 2 5 4 -5 A = and B=

A: Value of k , if AB=BA

Q: For F, = F + Fn-2 with initial condition Fo = Fi = 1, find F5? %3D

A: This can be calculated using recursion The tracing for F5 is as follows