Let g(t) be the staircase function of Fig. 7.5.15. Show that
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- (a) Draw an undirected graph G1 represented by the following adjacency matrix: 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 Does G1 contain a Hamiltonian cycle? Explain (b) Determine which pairs of graphs G1 in part (a) and G2 and G3 shown below are isomorphic and which are not, and explain your answer. If you use any invariant property in your argument, explain why this property is an invariant. Tex our answer. t 2 G2 G3 5. 7 8.arrow_forward2. Consider the Karnaugh map of a Boolean function k(w, x, y, z) shown at right. I (a) Use the Karnaugh map to find the DNF for k(w, x, y, z). (b) Use the Karnaugh map algorithm to find the minimal expression for k(w, x, y, z). x y z h(x, y, z) 0 0 1111OOOO: 0 0 0 0 нноонно 10 1 1 LOLOLOL 3. Use a don't care Karnaugh map to find a minimal representation for a Boolean expression h(x,y,z) agreeing with the incomplete I/O table below: 1 0 0 0 1 OLO 0 0 NE IN xy yz 1 IN WX yz 1 ÿz 1 wx wx wox xy xy fy 1 1 1 1arrow_forwardllowing function on the axes provided. f(x)={(-2 for x<=-4),(2x+1 for x>0):}arrow_forward
- ..arrow_forwardPlease solve.arrow_forwardGiven the following control points: (0 0 0); (0 1 0); (2 1 0); (2 0 0) and (1 0 0). The knot vectors are non-uniform and given as a. u=[0 00.5 13 3 3] b. u=[0 01113 3 3] Express the changes in the shape of the curve from the open-non-uniform case for K-3.arrow_forward
- 2. For the given Boolean function: F (A,B,C,D,E) = X(0, 2,3,4,5,6,7,11,15,16,18,19, 23,27,31) Show the area enclosed and label it with the corresponding literal, legibly. Obtain the simplest function in sum of product form and product of sum form using map methodarrow_forwardGiven the following function: f(x) = 2x For g(x) = Sf(x) dx, determine g(x).arrow_forward1. Assume that a function f is in polynomial time and can be computed in time 0(n) and that g is in polynomial time and can be computed in time 0(n°). Prove that f composed with g, that is f(g(x)), can be computed in time 0(n5).arrow_forward
- Consider the function f(x) = arctan(2(x − 1)) – In |x|. Plot (using PYTHON ) the graph of the function f(x) and describe the intervals of monotonicity of the function f. Speak also about the roots of the equation f(x) = 0. (a) (b) Prove by analytical means (using Calculus), that the equation f(x) = 0 has exactly four real roots P1 < P2 < P3 < P4.arrow_forwardFor each of the following pairs of functions ff and gg, circle one of the answers f \in o(g), f \in \Theta(g),fEo(g),fE0(g), or g \in o(f)g€o(f) f(n) = 2", g(n) = (;) Oƒ € o(g9) Oƒ€ 0(g) O gE o(f) %3D %3D i=log2 n f(n) = E" 2', g(n) =n Oƒ € o(g) Oƒ€ 0(g) O gE o(f) %3D %3D f(n) = (210 + 3n)², g(n) = n² Oƒe o(g) Oƒ€ 0(g) Oge o(f) %3D %3Darrow_forwardFind the length of the curve y = f (x), for:arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole