A set S of vertices is an independent set if there are no edges between any two vertices in S (e.g., vertices of a common color form an independent set). An edge cover is a set C of vertices such that every edge is incident to a vertex in C. Show that in a graph H with vertex set V, if S is an edge cover, then V-S is an independent set. can you explain with examples or drawing?

Q: 1.) An open box is to be made with a volume of 36,000 cm3. Find the least material or surface area…

A: Given : Volume=36,000 cubic centimeter. length=2×width Let, Length=l Width=w height=h Volume=l×w×h

Q: If F (2x + y)i + (3y 4x)j evaluate o. F.dr around a triangle ABC in the xy-plane with A(0. 0). B(2.…

A: Line integration of the function

Q: Let f(x) = |x| where xeR. Discuss the continuity and differentiability of f(x) at x = 0

A: discuss the continuity and differentiability of f(x) at x = 0 f(x) = | x |

Q: Problem 2. Consider the equation: x?y"(x)- xy' +y = 0. Given that yı(x) = x is a solution of this…

A:

Q: Consider the following maximization problem. Maximize P = 12x + y – 13z subject to the constraints…

A: Given that  Maximize P=12x+y-13zsubject to 12x-y+14z≤80                   x-13y+2z≤28…

Q: 15. How many combinations has a 3-digit lock? A. 27 B. 100 C. 300 D. 1000

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Consider the function 1 1- x4 Write a partial sum for the power series which represents this…

A:

Q: f(t) = sin* 3t A.G 12 24 + s2 +36 8 (s2 +144 B. 8 \s2+144 . (t 4s + s2 +36 c. * ) D.(14 12 24 С. 8…

A:

Q: Problem 7. Let f : N→ N be the function such that f(n) = 1 if n is a perfect cube, and f(n) = 0…

A:

Q: if f(z) = (ax – x³ + 3xy³)+ (by – 3x²y+ y') is anal ytic , then the value of a and is

A: We have , f(z) = ax - x3 + 3xy2 + iby - 3x2y + y3 We have given that ,  f  is analytic function.…

Q: what Is the gimplest form of 5i (1-i) (2-i) (3-i) a. -10i -5/3 C. b. -8i d. -V½

A:

Q: 3. Let å1, åz, åz be three nonzero vectors in R2 and let b1, b2, bz be three real numbers. Consider…

A:

Q: Determine the equation of the line that is tangent to y = = elan°(2x) at x =

A:

Q: f(t) = t sinh 5t 5s 5s С. (s2+25)2 А. (s2-25)2 10s 10s В. (s2-25)2 D.- (s2+25)2

A:

Q: Зх — 0.1у — 0.2z %3D 7.85 0.1х + 7y - 0.3z %3D —19.3 0.3х — 0.2y +10z %3D 71.4

A:

Q: f(t) = t cos 4t 8s 8s А. (s² –16)? С. (s2+16)2 s2+16 В. (s2 –16)2 s2-16 D. (s²+16)²

A: To find the Laplace transformation.

Q: If the Wronskian W of f and g is t'e", and if f(t) = t, find g(t). NOTE: Use c as an arbitrary…

A:

Q: 4. у + 2x &y(1) = 2. y3

A:

Q: Using the theorem on determinants, show that |1 а a? b b2 = (b – a)(c – a)(c – b) c2 A = 1 %3D

A:

Q: Find a primitive root (i.e. a primitive (p? – 1)st root of unity) in F3[i], and write down the…

A: F3i : It is the unique field of three elements. It can be defined as the ring of integers of modulo…

Q: Find the centroid of the solid of revolution obtained by rotating the region bounded by y=x^3, y=8,…

A: We have to find the centroid of solid.

Q: Is (P + Q) = (P= Q) a tautology? Explain.

A:

Q: To have more depositors, new investment products must be made to the small businesses and single…

A:

Q: 6x-7 4. S 를 In(4x2 + 1)-2 n(2x + 1)-승Tan-1(2x)| + C (2x+1)(4x2+1)

A: 4 Given integral is ∫6x−72x+14x2+1dx. First of all we will take a partial fraction of 6x−72x+14x2+1,…

Q: 3 2 -1 Rank of the following matrix is A = 4 2 6 7 4 5

A:

Q: ERROR CORRECTION TEST ITEM: DIRECTIONS: The entire test has been answered for you. Your job is to…

A:

Q: Find the solution. (D² - 20 - 3)y = 0; when x = 0, y = 0, y'= 4 A y = e-e B y =e+e y = e y = -e

A:

Q: what IS the absolute value 7 -2 +i ? a. -J5 C. I b. J5

A:

Q: 4. Determine the Fourier sine series of f(x) = x + 1 0<x <n

A: The given problem is to find the Fourier sine series of given half range periodic function. Given…

Q: Suppose that f: G → G such that f(x) = axa. Then fis a group homomorphism if and only if a = e O a^4…

A: Given that f:G→G be a function such that fx=axa

Q: What is the radius of convergence of the series below? 2-n (x – 1)" |n + 1 n=0

A:

Q: Find the chromatic numbers of the following graph Color the graph with chromatic number of colors.…

A: Given us a diagram so we can coloured it with diffrent colour since no two colour  can give to same…

Q: Find the solution. 2y" - 3y' + y = 0 A y = c e y = c e

A:

Q: FALSE and give a counterexample and justify or explain briefly why this is such. (a) Let A and B be…

A: Here we use examples and theorems for sequences.

Q: Find the Laplace Transform fit) = sin(2t) cos (2t) 2 A F(8) = g2– 16 B F(s) = s²+ 16 © F (s) = s2-…

A:

Q: Consider such a definition average distance, which is the average distance over all pairs of nodes…

A:

Q: a Prove that I = { : a,b,c,d are even integers} is an ideal of M2(Z). d

A:

Q: Use Gauss-Jordan Elimination to solve the following system. Identify the Gaussian Matrix and the…

A: We use Gauss-Jordan Elimination method to solve the given matrix.

Q: G1 = Z÷ and G2 = Z, *

A:

Q: 1. Find y'or for each of the following functions: dx 5 sin x 7-2 sin x (a) y : tan x (b)y =: 2x-3 3…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: One of the stationary points of the Uncuon Is this a maximum or minimum point of the graph?

A: Given: y=4x5-6x3+x2-2 The stationary point is (-1,1).

Q: Sketch the graphs of the following, inserting relevant values. 0 < x < 5 5 < x < 8 1 f (x) = {0 f(x+…

A:

Q: Measure and record the following masses b. 11 11 10 (1 kg) 10 (1 kg) 2 3 9. 3- Mass Mass (x 100g) (…

A: Given:

Q: Express the complex number below in polar form - 3+Jai ? a. 253 (cos s%G+ i sin sã ) 6. 3 + 3. d.…

A:

Q: Given the following matrices, perform the indicated matrix operation. 1 8 [5 1 -2 -9 7 1 2 -2 -4 5…

A:

Q: DIRECTIONS: The entire test has been answered for you. Your job is to check the answers for errors.…

A:

Q: 5. (Ci | Show that L{e"t"} = n! in two ways: (s- a)n+1 (a) Use the translation property for F(s).…

A:

Q: Q3) By using Graphical Method. Find the optimum solution of X1 and X2 that the maximize Z=X1 + X2…

A:

Q: what Is the conjugate of Js -J2i ? a. Jo -Joi d. -i b.Ja -ぶ

A:

Q: Prove the following statement using an element-chasing argument. If ACBUC and AN B= Ø then A C C.

A: Let x be any arbitrary element in the set A.  Then as A is a subset of B U C, x must be an element…